I think of it as the "noise floor" of probability. It's great that, say, the odds of a DNA match is one in a trillion, but the odds of someone getting there wrong sample, misreading the results, deliberately forging the results, etc. is so much higher that the probability really only tops out (or bottoms out, depending on your perspective) at the noise floor.

Comes up a lot in our world because computers so easily generate those large probabilities by being the things that can run millions of "samples" of some distribution per second, but you always have to cap those analyses to the probability noise floor or you'll be very misled.