Fog and dust are used to be considered as major performance degrading factors for free space optic (FSO) communication links. Despite the number of field measurements, performed in foggy environments during the last decades, most of the proposed channel attenuation models are deterministic, i.e., assumed the channel attenuation constant over time. Stochastic behavior of the channel is still understudied. In this work, we investigate the probabilistic behavior of the FSO channel in fog and develop a new statistical model for the signal attenuation. Moreover, we derive a probability distribution function (PDF) for the channel state. Using this PDF, we study the FSO system performance considering various metrics including average signal-to-noise ratio, average bit error rate, channel capacity, and probability of outage. Closed form expressions are derived for the average SNR and outage probability. We found acceptable performance with moderate and light fog. However, under thick and dense fog, the system performance poorly deteriorates. Finally, we derived closed form expressions for the average attenuation-distance product and the link availability that will potentially be very helpful for network design and planning.