rf-loop thanks for nice reply, but i did not speak about HF case (when folks use metal springs attached to probes to reduce ground path).
Just from the picture, when there are 2 probes and both are attached by the wire.. idk why attach 2nd wire if 1st is already ground to scope. And it's same ground point.. and the distance doesn't make an issues and freqs also guess. Just about that
In many simple LF cases one GND is enough. My previous answer was related to when a simple use of one probe's GND wire is not enough and for situations where the probe's "long" GND wire is not suitable at all.
Often (but not always), when just watching slow "easy" signals on several channels, it is enough (limited acceptable with notes) if the one GND wire of one probe is connected.
But also as BillyO well said...
If not really know... best to connect least all probes GND. It is also a good way to get used to the correct common practices. This way the user can avoid some of the traps that are offered around every corner..
And for end; If people do not know what he/she are doing and what is what and how things go.. connecting every probe GND is right way. (but also avoid ground loops and think how GND currents flow in DUT and how they may affect...)
As we know there is no simple answers and more details we go and deeper and deeper all goes more and more complex and finally infinite complex if go enough deep to details....