Given an alphabet $A = \{a_1, ..., a_n\}$ where the letters are not equiprobable, and two separate random word drawn from $N$ letters, is there a way to compute the probability that these two words would match up to $n$ errors?
Despite all my efforts I don't see any solution. However, since I am no expert, I want to know if there is a way to solve this analytically before I tackle it with a no-brain bootstrap approach.