  In this paper we create a model of particle motion on a three-dimensional
lattice using discrete random walk with small steps. We rigorously construct a
probability space of the particle trajectories. Unlike deterministic approach
in classical mechanics, here we use probabilistic properties of particle
movement to formally derive analogues of Newton's first and second laws of
motion. Similar probabilistic models can potentially be applied to justify laws
of thermodynamics in a consistent manner.
