  In the probability representation of the standard quantum mechanics, the
explicit expression (and its quasiclassical van-Fleck approximation) for the
``classical'' propagator (transition probability distribution), which
completely describes the quantum system's evolution, is found in terms of the
quantum propagator. An expression for the ``classical'' propagator in terms of
path integral is derived. Examples of free motion and harmonic oscillator are
considered. The evolution equation in the Bargmann representation of the
optical tomography approach is obtained.
