We define a sequence of mappings $\Gamma_k:D_0(R_+)^k\to D_0(R_+)^k$ and prove the following result: Let $N_1,\ldots,N_n$ be the counting functions of independent Poisson processes on $R_+$ with respective intensities $\mu_1 < \mu_2 < \cdots < \mu_n$. The conditional law of $N_1,\ldots,N_n$,…