i can only answer easier question:

given a random sequence of n numbers(not digits) what is the ppb, that this sequence is a valid siteswap. as every number mod n is equally propable. than we chose the numbers randomly. the first number can be chosen any way. the second can’t interfere with the first so it is (n-1)/n ppb , that it won’t be the reason that the sequence is not a siteswap. the third cant interfere with first, and second, so (n-2)/n

the ppb, that the given sequence of n random numbers is a siteswap is then n! / n^n.

but when you have digits only, than whole thing become much more compicated.

on the other side, when we consider siteswaps containing only digits there are only 2 possible siteswaps (zeros and ones)

so the longer alphabet(more digits), the bigger chance of finding siteswap?—strach