This paper deals with the problem of distributed fault detection for discrete-time sensor networks subject to randomly switching sensing topology. The system dynamics and sensing topology are modeled by a discrete-time Markov chain with incomplete transition probabilities. Each sensor node can effectively communicate with certain neighboring sensors, and randomly switch among finite sensing modes via the Markovian switching rules. The process or the time at which the sensing topology changes does not need to be known a priori. The Kronecker product is adopted to realize the decoupling between the specifical sensor node and its underlying neighboring nodes. By means of the Lyapunov functional approach and an improved free weighting matrix technique, stochastic analysis and design results on distributed fault detection, in terms of a set of linear matrix inequalities (LMIs), are then presented in the simultaneous presence of incomplete transition probabilities, randomly switching sensing topology, uncertain network-induced delays and accumulated data packed dropouts. A simulation example is finally provided to illustrate the effectiveness of the developed theoretical results.