The probabilistic approach to wave propagation starts in a way that is similar to ray theory, from the representation of the wave field as a product of the amplitude and of the exponent of the eikonal, which is computed by a canonical technique of analytical mechanics. However, an important difference is that the amplitude is not approximated but is represented by exact probabilistic formulas that admit efficient numerical evaluation, and that is a direct improvement of many asymptotic solutions. This approach is shown to be an effective tool for the analysis of numerous wave propagation problems, including those of wave diffraction by a screen occupying a plane angular sector and of electromagnetic diffraction by a wedge with anisotropic impedance boundary conditions.