This paper presents a stability concept of a class of discrete event systems (DESs) using Markov chains. The DESs under consideration are modelled as state machines adopted from Ramadge-Wonham, which represent the hybrid dynamic models of constrained motion systems. By identifying the probability of firing enabled events of the DES, p-convergence is proposed. Some properties of p-convergence are investigated including the fact that p-convergence is a generalization of the convergence proposed by Brave and Heymann yet it is less restrictive. The application of p-convergence is shown for a robotic assembly DES.