In this paper, we consider the distributed estimation problem by a set of agents connected by an arbitrary communication network. Specifically, the problem of reconstructing the conditional probability of the random state using the conditional probabilities communicated from other agents is discussed. It is discovered that in general the agents have to remember some of the past conditional probabilities and may even have to request additional informtion. A method for generating the fusion algorithm for each agent based on the network structure is presented and applied to some examples. The results are applicable to both dynamic and static states.