The problem of entity resolution over probabilistic data (ERPD) arises in many applications that have to deal with probabilistic data. In many of these applications, probabilistic data is distributed among a number of nodes. The simple, centralized approach to the ERPD problem does not scale well as large amounts of data need to be sent to a central node. In this paper, we present FD, a fully distributed algorithm for dealing with the ERPD problem over distributed data, with the goal of minimizing bandwidth usage and reducing processing time. FD is completely distributed and does not depends on the existence of certain nodes. We validated FD through implementation over a 75-node cluster. We used both synthetic and real-world data in our experiments. Our performance evaluation shows that FD can achieve major performance gains in terms of bandwidth usage and response time.