Here's a thought that has been sneaking in the back of my mind for a while: Is there a smallest possible nonzero probability, below which there is only zero probability?

Consider, for example, the wavefunction of an electron in the 1s orbital of a hydrogen atom. It is fairly straightforward to calculate the probability of finding that electron as a function of distance from the nucleus. This probability is non-zero at every point in the universe, but vanishingly small at any distance further than (for argument's sake) 10 Å. Is this universal existence real in any sense, or is this just an artifact of a model that is too simple? (it is often mathematically much simpler so integrate from 0 to ∞ and consider this a limit, than to actually plug in numbers and crunch)

This has implications--some of which are perhaps only philosophical, like if the calculated probability of an event is so small that it could only happen once in 10^{100} years--but some, like the coupling of wavefunctions through space (and time) for particle exchange or quantum entanglement could have actual measurable and practical ramifications.