Let $X_1,\dots,X_n$ be independent random variables with continuous distribution function $F(x)$, $$ F_n(t)=n^{-1}\sum_{i=1}^nI(t-X_i) $$ be an associated empirical distribution function and $V_n(t)$ be an empirical process: $$ V_n(t)=\sqrt n[F_n(t)-F(t)]. $$ In the paper the recurrent formula (5) for the probabilities $$ \mathbf P\{V_n(t)<h(t)\ \forall t\colon 0<F(t)<1\} $$ is given, where the function $h(t)$ supposed to be right-continuous. We use this formula for the computation of distribution functions of weighted Smirnov's statistics for a finite sample sizes (formulas (2) and (3)). The tables of percentage points of these distributions are given and a comparison with earlier results is made.