Why connect the grounds? Even if you have to connect them, use
inductors. The probes seems to be AC shorted.
For the same reasons as you can turn on one light in your house without
affecting the others even though all are connected together.
That may be true for 60Hz, but not for higher frequencies. At 10 Khz
(and harmonics), signals can travel in different paths. Unfiltered
power supplies are just AC shorts.
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