This article introduces novel and deep learning approaches for the security analysis of a hybrid satellite-terrestrial cooperative network. More specifically, a satellite transmits information to a ground user through multiple relays in the presence of an eavesdropper. To prevent potential eavesdropping, multiple friendly jammers are employed to disrupt the reception process of the eavesdropper by artificial noise. Within this setting, we then derive the closed-form expressions of the outage probability (OP) and secrecy outage probability (SOP) of the considered system in the presence of imperfect channel state information. Important to mention is the fact that in complex systems (e.g., with multiple jammers, multiple relays, and considering the independent but nonidentically distributed Rician nature of satellite links), analytical approaches may not be effective due to their complex mathematical derivations. As such, we develop a highly effective yet low-complexity deep learning approach to estimate the OP and SOP of the system. Through extensive Monte Carlo simulations, we evaluate the OP and SOP of the system in various settings and demonstrate the effectiveness of the proposed solutions. Interestingly, the proposed deep learning method can achieve comparable performance to that of the analytical approach.