The Internet of Things (IoT) connects smart objects so they can share information in a network to provide context-sensitive services. The amount of shared information will increase, likely dramatically, as more and more smart objects join the network and disseminate their contextual information. In this paper, we explain how smart IoT devices can share a large amount of context information using much less storage space and communication bandwidth. We use the versatile and simple JSON format at the application interface to allow applications to define their context descriptions, but we convert this JSON format into size-efficient yet equivalent probabilistic data structures for storage or communication. The loss of schema information in the conversion is compensated for by introducing a schema summary, which incorporates a hierarchical structure, and a state machine that recovers the schema information from the relationship among elements in a summary.