We consider the Kolmogorov equation associated with the stochastic Navier--Stokes equations in $3D$, we prove existence of a solution in the strict or mild sense. The method consists in finding several estimates for the solutions $u_m$ of the Galerkin approximations of $u$ and their derivatives. These estimates are obtained with the help of an auxiliary Kolmogorov equation with a very irregular negative potential. Although uniqueness is not proved, we are able to construct a transition semigroup for the 3D Navier--Stokes equations. Furthermore, this transition semigroup has a unique invariant measure, which is ergodic and strongly mixing.