A probability measure $\mu $ on a finite set R is called interior if $\mu (a) > 0$ for any $a \in R$. The set of all interior measures on R is denoted by $W(R)$.Theorem. There exists a mapping$\varphi $ of $W(R)$into Euclidean spaceEof suitable dimension with two properties1. All conditional probabilities\[ \mu (\left. a \right|A) = \frac{{\mu (a)}}{{\mu (A)}},\quad a \in A \subset R, \]are uniformly continuous functions$\varphi (\mu )$on the whole set$\varphi (W(R))$in the sense of the metric onE.2. The closure of $\varphi (W(R))$ in Eis homeomorphic to the closed simplex of suitable dimension