Due to their flexibility, aerial vehicles (AVs), such as unmanned aerial vehicles and airships, are widely employed as relays to assist communications between massive ground users (GUs) and satellites, forming an AV-relayed ground-air-satellite solution (GASS). In GASS, the deployment of AVs is crucial to ensure overall performance from GUs to satellites. This paper develops a stochastic geometry-based analytical model for GASS under Matern hard-core point process (MHCPP) distributed AVs. The 3D distributions of AVs and GUs are modeled by considering their locations on spherical surfaces in the presence of high-altitude satellites. Accordingly, we derive an overall connectivity analytical model for GASS, which includes the average performance of AV-relayed two-hop transmissions. Extensive numerical results validate the accuracy of the connectivity model and provide essential insights for configuring AV deployments.