The snapshot problem addresses a collection of important algorithmic issues related to distributed computations, which are used for debugging or recovering distributed programs. Among existing solutions, Chandy and Lamport have proposed a simple distributed algorithm. In this paper, we explore the correct-by-construction process to formalize the snapshot algorithms in distributed system. The formalization process is based on a modeling language Event B, which supports a refinement-based incremental development using RODIN platform. These refinement-based techniques help to derive correct distributed algorithms. Moreover, we demonstrate how other distributed algorithms can be revisited. A consequence is to provide a fully mechanized proof of the resulting distributed algorithms.