I think I see what you're saying. You're saying that if you do the math out, Pr(S) comes out to 0.5, just like 0! = 1 or a^0 = 1, even though the situation is rare where you'd actually want to calculate those things (permutations of zero elements or the empty product, respectively). Do I understand you, at least?

I expect Pr(S) to come out to be undefined, but I'll work through it and see. Anyway, I'm not getting any karma for these comments, so I guess nobody wants to see them. I won't fill the channel with any more noise.