From some random maths forum:
A statistical impossibility is a probability that is so low as to not be worthy of mentioning. Sometimes it is quoted as 10−5010−50 although the cutoff is inherently arbitrary. Although not truly impossible the probability is low enough so as to not bear mention in a rational, reasonable argument.
In some cases that arise in Gedanken experiments in thermodynamics, the probabilities can be approximately 10−Avogadro's number10−Avogadro's number, that is, 10−102310−1023, give or take a few billion orders of magnitude.The standard framework of probability theory attempts to assign to each outcome X� a number P(X)�(�) between 00 and 11, which we call the probability of the outcome. The higher the number, the more likely that outcome is to occur. Depending on context, a sufficiently small value of P(X)�(�) will correspond to something being improbable, but there's no inherent threshold between improbable and likely.
General probability theory does not have a good way of making sense of "impossible" or "necessity". Having a probability of 00 does not mean something cannot happen, and having a probability of 11 does not mean that something must happen. To explain this with a metaphor from geometry, consider the notion of area. The area of nothing is 00, but so is the area of a single point. In that sense, the notion of area cannot distinguish between nothing and that which is "infinitely small".
Similarly, when trying to applying probability theory to problems that have infinitely many outcomes, the probability of an event can be zero even if it is possible, so long as there are infinitely many other possibilities that are just as likely (or some similar situation). When it comes down to it, the real number line does not have infinitely small numbers, and since probability theory uses real numbers, these events can only be assigned a probability of 00.