Probabilistic origin of the laws of Mechanics and Relativity: In a diffusion with exclusion principle, the brownian bridges propagate pressure wavelets which interfere and make wave packets of which the group velocity Vgtends to equal the expansion velocity v of the Huygens sphere envelope of these wavelets. This convergence Vg> v due to the strong large numbers law involves the Galilean and Lorentz groups, the limit Vg=v is reached on monochromatic waves and stationary states.