Hahahaha, yes, I know it seems insane but the electrons don't touch each other, that doesn't mean that they don't move. When you cut yourself your electrons and electrons in the knife are moving but no, they are not touching :)

Electrons moving with probability - that seems complicated and... scary.

They are not moving. They are disappearing in one place and appearing in another one. We can determine what is the probability to find them in one place or another. Welcome to quantum physics :D