Verifying distributed algorithms is non trivial. A promising methodology is based on the Event B language and the refinement process : it consists in redeveloping the algorithms by targeting a collection of required properties, using the refinement of models which preserves the properties of an abstract one in concrete ones. This approach has already been followed by Abrial et al for their work on the IEEE 1394 protocol. Our goal is to integrate probabilities into this approach. It appears that there are other proposals for dealing with this problem. This paper presents an illustration of our approach through the study of vertex coloring algorithms, based on an algorithm cited by Métiver et al, and preliminary elements of a global methodology on realistic distributed algorithms.