In this note, the problem of event-based state estimation for a finite-state hidden Markov model under a generic stochastic event-triggering condition and an unreliable communication channel is investigated. The effect of packet dropout is characterized with a Gilbert-Elliott process. Utilizing the change of probability measure approach, the packet dropout model and the event-triggered measurement information available to the estimator, analytical expressions for the conditional probability distributions of the states are obtained, based on which the optimal event-based state estimates can be further calculated, together with a closed-form expression of the average sensor-to-estimator communication rate. The effectiveness of the proposed results is illustrated by an application to a wireless automated machine health monitoring problem.