Voltage dip state estimation (VDSE) tries to estimate the voltage dip characteristics at nonmonitored buses from measured voltage dip values at monitored buses. In this paper, the VDSE is addressed through the method based on Bayesian inference. A priori including the fault position among other grid conditions is used to estimate the residual voltage at each bus based on the measurement quantities, including their uncertainties. The dip duration is calculated with the time setting of protection system incorporating the uncertainties due to dip detection algorithm of the root mean square values. The proposed method has been applied to the IEEE 13-bus and IEEE 123-bus distribution test systems for multiple simulation scenarios, such as with or without distributed generation and different types of faults. The simulation results show good observability of the network.