But, something like this should never happen with a probe.
But it does, everything has a breaking point, even the quality ones break with continued use or misuse.
What you have there is a cheap and dangerous probe. Best would be to replace it, and its black companion with something safe.
I'd concur, from both a safety and functionality angle. With better leads the insulation will usually be intact long after stress failure has open circuited the copper conductor. Better name brand leads may cost more but they will stand up to years more stress, stretch, tug and flex than the Won Hunglo copies.
... What you have there is a cheap and dangerous probe....
Yeah, but....
The other end of the cable is attached to the meter. If the cable breaks as shown, there's no danger except for not getting the reading you're expecting. The exposed end of the wire won't have high voltage on it under any circumstance.
I agree the probes are crap and should be replaced, but I wouldn't call them dangerous.
There can be plenty of danger, as you've stated, the other end is likely connected to the meter, which could be connected to anything. Not all voltage measurements are to ground, current measurement as already mentioned are generally made withing the active/positive lead. A test instrument needs to be trusted, who wants to trust something intermittent or far too fragile for reasonable use.
Quick Tip for leads of any quality. DO NOT tightly wrap then around your meter every time your finished with it! (No matter how much those moulded grips on your Fluke holster look like they are meant to do this. )
Most failures occur at the ends near the probes or plugs, every time you tight wrap your leads around your meter you are straining them far more than you ever will in normal use.