Why is the 1000v safe? My guess is energy released is small e.g. a small capacitor. Or internal resistance is high so it becomes much less when you touch it. Or you mean touch one end and it is DC.

I'm no EE, but my understanding is that it's partially because the amperage is very low and partially because the signal is AC operating at a frequency that causes a large impedance mismatch between the probe and people.

It's counterintuitive enough that the probes actually have an "anti-warning" label to inform people that they are safe to touch.