As the binary sensing model is a coarse approximation of reality, the probabilistic sensing model has been proposed as a more realistic model for characterizing the sensing region. A point is covered by sensor networks under the probabilistic sensing model if the joint sensing probability from multiple sensors is larger than a predefined threshold ε. Existing work has focused on probabilistic point coverage since it is extremely difficult to verify the coverage of a full continuous area (i.e., probabilistic area coverage). In this paper, we tackle such a challenging problem. We first study the sensing probabilities of two points with a distance of d and obtain the fundamental mathematical relationship between them. If the sensing probability of one point is larger than a certain value, the other is covered. Based on such a finding, we transform probabilistic area coverage into probabilistic point coverage, which greatly reduces the problem dimension. Then, we design the ε-full area coverage optimization (FCO) algorithm to select a subset of sensors to provide probabilistic area coverage dynamically so that the network lifetime can be prolonged as much as possible. We also theoretically derive the approximation ratio obtained by FCO to that by the optimal one. Finally, through extensive simulations, we demonstrate that FCO outperforms the state-of-the-art solutions significantly.