In this paper, we propose a compositional framework for the construction of discrete-time nite abstractions, also known as nite Markov decision processes, from continuous-time stochastic hybrid systems by quantifying the distance between their outputs in a probabilistic setting. The proposed scheme is based on the notion of stochastic simulation functions, which is used to relate continuous time stochastic systems with their discrete-time counterparts. Accordingly, one can employ discrete-time abstract systems as substitutions of the continuous time ones in the controller design process with guaranteed error bounds on their output trajectories. To this end, we first derive sufficient small-gain type conditions for the compositional quantication of the probabilistic distance between the interconnection of original continuous-time stochastic hybrid systems and their discrete-time (nite or innite) abstractions. We then construct nite abstractions together with their corresponding stochastic simulation functions for a particular class of nonlinear stochastic hybrid systems having some stability property. We illustrate the eectiveness of the proposed results by applying our approaches to the temperature regulation in a circular building and constructing compositionally a discrete-time abstraction from its original continuous-time dynamics in a network containing 1000 rooms. We employ the constructed discrete-time abstractions as substitutes to compositionally synthesize policies regulating the temperature of each room for a bounded time horizon.