With large sets or sequences of numbers approaching almost infinity, counting as a method of determining how large things are ... doesn't work well as you found out. To determine if ginormous set A is larger than ginormous set B, you have to do things like matching-pairing. For every element in set A, pair it with an element of set B; if you exhaust all of the elements in B but still have elements in A... then set A is larger than set B.

To formulate the probability of B happening, for example, you have to make an educated guess. Create a functional equation that map A (all possibilities) to B (desired possibility). Then you make a ratio-fraction with the equation in the numerator and set A in the denominator. Using Algebra, try to eliminate references to A in both the numerator and denominator to give you an educated guess of what the probability is.