In this paper, the privacy problem of a tandem distributed detection system vulnerable to an eavesdropper is proposed and studied in the Bayesian formulation. The privacy risk is evaluated by the detection cost of the eavesdropper which is assumed to be informed and greedy. For the sensors whose operations are constrained to suppress the privacy risk, it is shown that the optimal detection strategies are likelihood-ratio tests. This fundamental insight allows for the optimization to reuse known algorithms extended to incorporate the privacy constraint. The trade-off between the detection performance and privacy risk is illustrated in an example.