Autonomous agents rely on sensor data to construct representations of their environments, essential for predicting future events and planning their actions. However, sensor measurements suffer from limited range, occlusions, and sensor noise. These challenges become more evident in highly dynamic environments. This work proposes a probabilistic framework to jointly infer which parts of an environment are statically and which parts are dynamically occupied. We formulate the problem as a Bayesian network and introduce minimal assumptions that significantly reduce the complexity of the problem. Based on those, we derive Transitional Grid Maps (TGMs), an efficient analytical solution. Using real data, we demonstrate how this approach produces better maps than the state-of-the-art by keeping track of both static and dynamic elements and, as a side effect, can help improve existing SLAM algorithms.