With the fast increase of solar energy plants, high quality short-term forecast is required to smoothly integrate their production in the electricity grids. Usually, forecasting systems predict the future solar energy as a continuous variable. But for particular applications, such as concentrated solar plants with tracking devices, the operator needs to anticipate the achievement of a solar irradiance threshold to start or to stop their system. In this case, binary forecasts are more relevant. Moreover, while most forecasting systems are deterministic, the probabilistic approach provides additional information about their inherent uncertainty that is essential for decision making. The objective of this work is to propose a methodology to generate probabilistic solar forecasts, and more specifically the presence of clouds, as a binary event for very short-term horizons between 1 and 30 minutes. Among the various techniques developed to predict the solar potential for the next few minutes, sky imagery is one of the most promising. Therefore, we propose in this work to combine a state-of-the-art model based on a sky camera and a discrete choice model to predict the probability of cloud presence. Two well-known parametric discrete choice models, logit and probit models, and a machine learning technique, random forest, were tested to post-process the deterministic forecast derived from sky images. All three models significantly improve the quality of the original deterministic forecast. However, random forest gives the best results and especially provides reliable