We will focus on the formation of extreme waves in the open sea, adopting a probabilistic point of view. We will first identify the first term of the asymptotic development of the probability of occurrence of such a wave when the wave height tends to infinity. If an extreme wave occurs, what is the most likely mechanism that produced it? We will answer this question using two toy models. In the case of an integrable system, we will show that a linear superposition mechanism is the most likely. In the case of a strongly resonant system, the main formation mechanism is a nonlinear focusing effect, which induces an increase in the probability of occurrence of large waves.