Non-terrestrial Networks (NTNs) refer to the networks, where either satellites or unmanned aerial vehicles (UAVs) are deployed to extend the current terrestrial networks for serving the growing mobile broadband and machine-type communications. With the advantages of UAVs’ flexibility and satellites’ global coverage, the solution of UAV-To-satellite communications (U2SC) can provide promising global communication services for the emerging NTNs. Previous literature has explored many potential directions of U2SC, including channel tracking, deployment design, and link analysis. However, as a vital role in system performance, the connectivity of U2SC has not been well investigated yet. This research gap motivates us to present an analytical model to evaluate the connectivity of U2SC. In particular, we first present the system model of the U2SC by considering the distribution model of UAVs, antenna models, and the path loss model. We then utilize stochastic geometry to derive a theoretical formulation of the successful connection probability of U2SC. The comprehensive numerical results are given to evaluate the received power, the interference, and the successful connection probability of U2SC and analyze the impacts of system parameters, such as the number of frequency carriers, the type of frequency bands, the number of UAVs, and the satellite altitude.