The notion of probabilistic network has been used to characterize the unpredictable environment in wireless communication networks or other unstable networks. In this paper, we are interested in the problem of placing servers in probabilistic networks subject to budget constraint, so as to maximize the expected number of servable clients that can successfully connect to a server. We study this problem in both the single-hop model and the multi-hop model. We discuss the computational complexity of this problem and show that it is NP-hard under both models.We then develop efficient approximation algorithms, which produce solutions provably close to optimal. If the costs of candidate locations are uniform, when extra budget is available in the future, the progressive feature of our algorithms allows for placing additional servers instead of relocating all the servers, while retaining the guaranteed performance. Results of extensive experiments on different topologies confirm the performance of our algorithms compared to the optimal algorithm and other heuristic algorithms.