[math-fun] Probability distributions sought

For t > 0, let X(t) be a random variable with cumulative distribution function F(t,x) = Pr[X(t) <= x]. I am looking for X(t) (or equivalently, F(t,x)) with the following property: Given any set I = {t[i], i = 1 to N}, Pr[X(t[1]) > Max[X(t[i]), i = 2 to N]] = t(1) / Sum[t[i], i = 1 to N] Even X(t) that works for N = 3 would be helpful. Here is an example that works for N = 2 (but fails for larger N): F(t,x) = 1 - Exp(-x/t) Pr[X(u) > X(v)] = u / (u + v) With N = 3: Pr[X(u) > Max[X(v), X(w)]] = u^2 (uv+uw+2vw) / ((u+v)(u+w)(uv+uw+vw) Paul