The paper solves the problem of minimization of the Kullback divergence between a partially known and a completely known probability distribution. It considers two probability distributions of a random vector $(u_1,x_1,...,u_T,x_T)$ on a sample space of $2T$ dimensions. One of the distributions is known, the other is known only partially. Namely, only the conditional probability distributions of $x_{\tau }$ given $u_1,x_1,...,u_{\tau -1},x_{\tau -1},u_{\tau }$ are known for $\tau =1,...,T$. Our objective is to determine the remaining conditional probability distributions of $u_{\tau }$ given $u_1,x_1,...,u_{\tau -1},x_{\tau -1}$ such...