We propose a new probabilistic coverage protocol (denoted by PCP) that considers probabilistic sensing models. PCP is fairly general and can be used with different sensing models. In particular, PCP requires the computation of a single parameter from the adopted sensing model, while everything else remains the same. We show how this parameter can be derived in general, and we actually do the calculations for two example sensing models: (i) the probabilistic exponential sensing model, and (ii) the commonly-used deterministic disk sensing model. The first model is chosen because it is conservative in terms of estimating sensing capacity, and it has been used before in another probabilistic coverage protocol, which enables us to conduct a fair comparison. Because it is conservative, the exponential sensing model can be used as a first approximation for many other sensing models. The second model is chosen to show that our protocol can easily function as a deterministic coverage protocol. In this case, we compare our protocol against two recent deterministic protocols that were shown to outperform others in the literature. Our comparisons indicate that our protocol outperforms all other protocols in several aspects, including number of activated sensors and total energy consumed. We also demonstrate the robustness of our protocol against random node failures, node location inaccuracy, and imperfect time synchronization.