Malicious and selfish behaviors represent a serious threat against routing in Delay or Disruption Tolerant Networks (DTNs). Due to the unique network characteristics, designing a misbehavior detection scheme in DTN represents a great challenge. In this paper, we propose PMDS, a probabilistic misbehavior detection scheme, for secure DTN routing. The basic idea of PMDS is introducing a periodically available Trusted Authority (TA), which judges the node's behavior based on the collected routing evidences. We model PMDS as the Inspection Game and use game theoretical analysis to demonstrate that, by setting an appropriate investigation probability, TA could ensure the security of DTN routing at a reduced cost. To further improve the efficiency of the proposed scheme, we correlate detection probability with a node's reputation, which allows a dynamic detection probability determined by a node's reputation. The extensive analysis and simulation results show that the proposed scheme substantiates the effectiveness and efficiency of the proposed scheme.