Hi Diegooo1972, your message is a bit confusing, but let me see if I can help you to clarify your questions so the people that actually know about this stuff can help you out.
I see two things here:
1) EARTH GROUND
You CAN use a cable with no ground in your oscilloscope but it's not recommended unless you know EXACTLY what you're doing.
If the cable that provides power doesn't have a ground pin (or you avoid it using an adapter) you will leave your oscilloscope "floating" so it could be at a different potential from you.
If you're messing with low voltage electronics, it shouldn't be a problem (as the risk of getting shocked is low) but could put you in a path were you feel confident that it's always safe to do that.
Additionally, I see very few scenarios where this is really needed --> in a nutshell, you should understand that it's not a good idea and avoid it.
2) How to connect the probe leads
When you use the cable with the 3rd pin to power your oscilloscope, there's definitely a connection between EARTH ground and the ground in your probes.
In general that's not a problem (it only sets the "zero" level for the whole system) the REAL problems occur when you forget that:
a) All probes share the same ground, all channels in your oscilloscope are connected to each other through there.
b) if you connect any probe's ground to the power rail in your device and you have one of the probes connected to the "negative" side of your device, you will be shorting that rail.
I hope this will help you getting this thread going and some answers for you.
In any case, there's a very good video from Dave (EEVBLOG) where he explains all of this in detail... I recommend that you look for it in YouTube and then come back with some more questions