If someone is a three time felon and they only put a finger on a gun can they go to jail even if he didn't threatened anyone with it?

It depends on state laws and whether they are on probation or not. Under certain conditions it might be possible.

Wouldn't it depend on if this person is on probation and also the terms of the probation? Or is probation a standard set of rules? If your not allowed to be in possession of a weapon then yes, it violates it.

How likely is it that someone put one finger on a gun? If the person was found with a gun on them then yes that person violated the probation.