I have read the second answer of this MO post https://mathoverflow.net/questions/115278/minimum-1st-neghbors-distance-between-n-random-points-on-a-ring/115288#115288.
In the mid of Volkov's proof, he said ${\mathbb P}(\min_i W_i>a,W_1+...+W_K \in [L,L+\delta]) = \delta \frac{(L-Ka)^{K-1} e^{-L} }{(K-1)!}$ for infinitesimally small $\delta>0$. Those $W_i$'s are just i.i.d. $Exp(1)$ distributions. I know results of exponential distrubition like $W_1+...+W_K$ is Erlang distributed and $\min_i W_i$ is $Exp(K)$ distributed, but how to get his equation exactly?
Thank you so much in advance!