When I checked before the voltage on the VCC and GND on the NE555 there was a voltage around 13V DC.
What you thought was GND was -320V, and what you thought was +13V was -320V +13V, ...so bang!
If I didn't found out why that happend, I cant be sure how to make my steps in the future and not to be in danger.
Draw the diodes of a bridge rectifier, and follow where the main's live +/- 320V goes.
(https://i.imgur.com/RqpPy4N.jpg)
When you are sketching a diagram to see if you can figure out what is and isn't safe to connect a scope probe to, be careful to use the right ground symbol! If you use the wrong one you'll confuse yourself and think that points with a potential difference between them are actually at the same voltage.
(https://upload.wikimedia.org/wikipedia/commons/thumb/0/08/IEC_GND.svg/120px-IEC_GND.svg.png) (https://upload.wikimedia.org/wikipedia/commons/thumb/a/af/IEC_Chassis.svg/120px-IEC_Chassis.svg.png) (https://upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Low_noise_GND_2.svg/120px-Low_noise_GND_2.svg.png)
Earth Ground Chassis ground Common or Signal 'ground'
Only Earth ground is a true ground. That's the one where eventually you can trace it back to a large chunk of metal driven into the earth, (and not into a plastic flowerpot |O :-DD) Its what's your incoming mains supply is referenced to. In many countries there will be a Neutral to Ground bond somewhere in the supply system, and Neutral will *NORMALLY* be held within ten volts or so of Ground, except if there is a fault. In other countries the Neutral to Ground relationship wont be so well defined, and you may even be supplied with two phases of a three phase supply. You can bet there is a ground somewhere even if both your supply wires are at a high voltage relative to it. Learn what the local electrical code requires and what the actual situation is at the socket supplying your bench.
The other two symbols are chassis ground, and common or signal 'ground'. Chassis ground is the right one to use if there is a connection to a metal frame or case that may not actually be Earth grounded. You don't expect it to be reliably connected to ground, but you also don't expect there to be a significant voltage between it and true ground. Common or signal 'ground' is a much woollier concept, and is where the danger can be. E.g. in a single supply OPAMP circuit, your signal 'ground' is typically held at half the supply voltage.
On the primary side of a SMPSU, the Common (lets stop calling it a 'ground') is almost invariably the negative terminal of the bridge rectifier. Draw it out with the bridge rectifier, reservoir capacitor, and any transformers and optocouplers shown in full detail as individual component symbols (including all the diodes inside the rectifier), and the rest shown as functional blocks. Include the supply with the supply ground, and if you have a grounded neutral, show that but with a resistor between the earth Ground symbol and Neutral to remind you that Neutral is probably not actually be at 0V with respect to Ground.
Now you can work out what voltage difference to expect between your scope input, which normally has the connector shell, and thus the probe ground clip grounded to chassis, and the chassis connected to the supply Ground wire, traceable all the way back to earth Ground, and the circuit you want to probe.
If you draw it out, in many European countries, you'll find a SMPSU common is banging up and down at 50Hz between somewhere near 0V and about -310V with respect to earth Ground. In the USA it will be banging up and down at 60Hz between near 0V and -160V unless the PSU uses a voltage doubler, in which case its probably sitting at -160V. In other countries its banging up and down between less well defined voltages, but still more than 1.4 x your RMS AC supply voltage apart. In all cases shorting it to a true Ground is a *BAD* *IDEA* and hundreds of amps can flow for that brief period before the supply breaker trips or fuse blows.
Even if you *expect* the circuit to be truly Grounded, unless you are 100% certain its connected to the same Ground point as your scope, check the voltage between your scope ground and where you are going to clip the ground lead to, on your meter on *both* AC and DC voltage ranges. If there is a difference you should investigate further - if its a few volts AC or DC, try a small torch bulb between a known good true Ground and your scope ground, and also between your true Ground and the circuit. If it glows at all there is a ground offset and a low enough impedance to drive significant current if you short it, so *STOP*. If it doesn't light or glow at all and the bulb filament still tests good, its OK to connect your scope ground to the circuit. If you see an AC voltage of around half your supply voltage, (give or take a large margin), but no DC voltage, its probably AC leakage through class Y EMI filter caps. Take a small mains appliance bulb and check as above. If you see a large DC voltage, *STOP* immediately.
The series string of resistors need to be in parallel with (across) the meter input jacks.
Take a small plastic project box and a pair of cheap multimeter leads. Lay the leads across the box and check the meter end is going to be long enough to reach the meter sockets without straining the wires. Mark the leads in the center of where they cross the box. Cut the leads there. Drill the box half way up its sides, two holes in each long side, one at either end to feed the leads in and out the other side. Rough up the inside of the box round the holes with sandpaper. Thread the cut lead ends in through the holes and pull through enough length to work with. Strip 1/2" of the end of each lead. Solder the four 4K7 3W wirewound resistors together in series, twisting each joint before soldering, then slip some glassfibre heat resistant sleeving over the whole lot. For heat resistant supports for the resistor, take two pieces of thin ceramic tile, cut rectangles that just fit inside the box vertically and take up the full width, and drill one hole through the middle of each of them (use a small glass drill). Thread them onto the resistor assembly end leads. Twist and solder both red wire ends to the protruding resistor lead, then the same with the black wires, to the other resistor lead. Glue the tiles in place with Epoxy or silicon caulk so the resistors cant touch the sides of the box. Pull the wires tight, and fit a cable tie right up against the box inside wall at each hole so they cant be pulled out. Secure each wire to the box wall at the cable tie with a blob of epoxy or silicon caulk. Let all the glue set. Screw the lid on the box and label it:
Low Impedance Voltage Test Lead for DMM
Max 500V for FIVE seconds
Check resistance before use: 18.8K (nom)
Usage is as described earlier.
The risk is minimal as long as you use a known good earth ground point for the tests. If you aren't sure if a ground point is good don't use it. Worst case: take a mains plug, and a length of hookup wire, connect the hookup wire to the ground pin, and screw the other two terminals down tight so the screws cant come loose, bulk up the hookup wire with rubber tape till the plug's cord grip can grip it securely, reassemble the plug, and use that, plugged into the same wall socket plate (or an extension off it) as your test bench equipment, and use the free end of that hookup wire as your test earth ground, AFTER checking the socket with a socket tester.
How much voltage is too much? Well that depends. Once you get below about 10V its not the voltage that's the problem, its how much current it can supply, which is why you then need to do the torch bulb test. If the bulb lights, even dimly (or blows), *DONT* proceed with connecting the scope ground to that point. Don't try to measure the leakage current with a multimeter - that's a good way to blow $expen$ive$ multimeter fuses if its more than expected.
If the above description of the apparatus required and methods to use it is still incomprehensible to you then *PLEASE* do not attempt to do any work on mains circuits or PSUs except under the direct supervision of a trained and qualified Electronic or Electrical appliance repair technician, with teaching experience.