Degraded visual environments have strong impacts on the quality of LiDAR data. Experiments in artificial fog conditions show that noise points caused by water particles present various distance distributions which depend on visibility. This article introduces a mathematical framework based on Bayesian inference and Markov Chain Monte-Carlo sampling to infer optical visibility from point clouds. The visibility estimation is cast as a classification problem based on the identification of the distance distributions. Contrary to deep learning methods, our approach is model-based and focuses on the design of a full probabilistic framework, more comprehensible, which is critical for autonomous driving. Ultimately, the impact of the optical visibility on the probability of detection of standard targets is assessed, which can yield improvements on autonomous vehicles performances in adverse weather conditions.