To identify objects shared by entities and to, in turn, identify free space in nonvolatile storage, a computer system uses a probabilistic data structure which tests whether an element is a member of a set. Such probabilistic data structures are created for entities in the storage system that share objects. The probabilistic data structure for an entity represents the objects that are used by that entity. When an entity is deleted, each object used by that entity is compared to the probabilistic data structures of other entities to determine if there is a likelihood that the object is used by one or more of the other entities. If the likelihood determined for an object is above an acceptable threshold, then the object is not deleted. If the likelihood determined for an object is below the set threshold, then the object can be deleted and the corresponding storage locations can be marked as free.