Address event representation (AER) image sensors represent the visual information as a sequence of events that denotes the luminance changes of the scene. In this paper, we introduce a feature extraction method for AER image sensors based on the probability theory, namely, bag of events (BOE). The proposed approach represents each object as the joint probability distribution of the concurrent events, and each event corresponds to a unique activated pixel of the AER sensor. The advantages of BOE include: 1) it is a statistical learning method and has a good interpretability in mathematics; 2) BOE can significantly reduce the effort to tune parameters for different data sets, because it only has one hyperparameter and is robust to the value of the parameter; 3) BOE is an online learning algorithm, which does not require the training data to be collected in advance; 4) BOE can achieve competitive results in real time for feature extraction (>275 frames/s and >120,000 events/s); and 5) the implementation complexity of BOE only involves some basic operations, e.g., addition and multiplication. This guarantees the hardware friendliness of our method. The experimental results on three popular AER databases (i.e., MNIST-dynamic vision sensor, Poker Card, and Posture) show that our method is remarkably faster than two recently proposed AER categorization systems while preserving a good classification accuracy.