"""An infinite amount of time would imply infinite probability"""
Is this true? I can see where you are coming from - but surely some things within the confines of a physical universe are simply "impossible". Physical laws have a limit, a boundary if you like and thus, this would imply that their is a finite number of possibilities. Infinite time in itself would not be enough.
If I placed the principle materials of a car in a hole in the ground would "infinite time on its own" produce a fully working car? This surely is not improbable but actually impossible!
But you are right - infinite time opens the way to possibilities way beyond our comprehension.