Let V k = u 1 u 2 ⋯ u k , u i 's be i.i.d ∼ U(0, 1), the p.d.f of 1−V k+1 be the GF of the unsigned Stirling numbers of the first kind s(n, k). This paper discusses the applications of uniform distribution to combinatorial analysis and Riemann zeta function; several identities of Stirling series are established, and the Euler's result for ∑H n /n k−1, k ≥ 3 is given a new probabilistic proof.