This letter investigates the secrecy outage performance of satellite-to-terrestrial downlink transmissions consisting of one legitimate receiver (D) and one eavesdropper (E). To reflect the practical application scenarios, it is assumed that D and E are randomly distributed in the footprint of the satellite. Furthermore, in the considered downlink scenario, D and E are equipped with multiple antennas, and maximal ratio combining (MRC) technique is adopted at both of them to seek the maximum receiving diversity gain. To reveal the impacts of the randomness of the positions of D and E, and MRC scheme on the secrecy outage performance of the considered satellite-terrestrial system, the exact and asymptotic closed-form analytical expressions for secrecy outage probability are derived by using stochastic geometry method. Finally, simulation results are given to confirm the accuracy of our proposed analytical models.