Human drivers are endowed with an inborn ability to put themselves in the position of other drivers and reason about their behavior and intended actions. State-of-the-art driving-assistance systems, on the other hand, are generally limited to physical models and ad hoc safety rules. In order to drive safely amongst humans, autonomous vehicles need to develop an understanding of the situation in the form of a high-level description of the state of traffic participants. This paper presents a probabilistic model to estimate the state of vehicles by considering interactions between drivers immersed in traffic. The model is defined within a probabilistic filtering framework; estimation and prediction are carried out with statistical inference techniques. Memory requirements increase linearly with the number of vehicles, and thus, it is possible to scale the model to complex scenarios involving many participants. The approach is validated using real-world data collected by a group of interacting ground vehicles.