Hmm, well looking at it from a computer science/mathematical background, I would calculate the probability P of a "false positive" like this:
Two strings X and Y of length L are identical for all but N places. What is the probability that for a sequence of length S, starting at a random position r along the length of the strand, that the substring X[r... r+S] is identical to the substring Y[r ... r+S]. In other words P is a function of L, N, and S, P(L, N, S) The percentage similarity would be (L-S)/L. Thats would be pretty hefty calculation to work through - calculating every single combination of the positions of difference. For instance the probability is much greater if all the differnces are "packed " in one location at the begging of the string. Then there are a lot more ways to get a match than (the first S substrings would be different, but the rest of the L-S substrings would produce a match. If the differences are distributed evenly, the probability is at a minimum, and could even be zero if S is large enough(though not for DNA). For example if L was 10, N was 1, and S was 5, placing the difference at position 5 would mean that NO substring of length 5 could ever match, but if you put it at position 1, then then you have 4 different possible substrings that are matches {2..7, 3..8, 4..9, 5...10 }
Of course, all this rests on certain assumptions, that the distrubution of differences for the two strands is random, that you start making comparisons in a random place, and that all comparisons are 100% accurate. I know that comparisons aren't 100% accurate(there are errors in transcription), as it would be impoosible to get a "false negative" (although it very nearly is). I also suspect that the distribution of difference is not completely random as well, certain mutations would be lethal and don't occur. And I believe there are "markers" used in finger printing so sequencing does not take place at random position along the the string. And of course, human DNA is not one long continuous strand but is broken up into 23? chromosones.