In this letter, we extend our previous analytical results (Mikula & Niebur, 2003) for the coincidence detector by taking into account probabilistic frequency-dependent synaptic depression. We present a solution for the steady-state output rate of an ideal coincidence detector receiving an arbitrary number of input spike trains with identical binomial count distributions (which includes Poisson statistics as a special case) and identical arbitrary pairwise cross-correlations, from zero correlation (independent processes) to perfect correlation (identical processes). Synapses vary their efficacy probabilistically according to the observed depression mechanisms. Our results show that synaptic depression, if made sufficiently strong, will result in an inverted U-shaped curve for the output rate of a coincidence detector as a function of input rate. This leads to the counterintuitive prediction that higher presynaptic (input) rates may lead to lower postsynaptic (output) rates where the output rate may fall faster than the inverse of the input rate.