Floating Content (FC) is a paradigmatic example of opportunistic infrastructure-less content sharing system where information is spread upon mobile node encounters within an area which is called the replication zone. FC allows the probabilistic spatial storage of information, even in the case of unreliable communications, with no support from dedicated servers. Given the large amount of communication and storage resources typically required to guarantee content persistence despite node mobility, a major open issue for the practical viability of FC and of similar distributed storage systems is the characterization of their storage capacity, i.e., of the maximum amount of information which can be stored for a given set of system parameters. In this paper, we propose a simple yet powerful information theoretical model of the storage capacity of probabilistic distributed storage systems such as FC, based on a mean field model of opportunistic information exchange. We evaluate numerically our results, and validate the model by means of realistic simulations, showing the accuracy of our mean field approach and characterizing the properties of the FC storage capacity versus the main system parameters.