The number of space objects has largely increased in the recent years, becoming a considerable threat to the present and future of satellite operations and human spaceflight. This introduces a need to accurately compute the risk of collision between satellites and space debris. Current methodologies are limited by the type of encounter and the vehicle shape, usually simplified by a sphere. These assumptions rely mainly on linearization of the dynamics and simplification of the uncertainty distribution as a Gaussian function. Developing a collision probability calculation method that overcomes these limitations and provides high-accuracy results is the topic of this work. The methodology developed follows a hybrid combination of trajectory propagation and statistical methods for uncertainty propagation. With the propagation method covariance information of the satellite position and velocity will be available. Finally, the method is adapted to any satellite geometry by developing a numerical quadrature technique based on a combination of spheres to model the real body shape. The combination of these methodologies to compute the collision probability has been verified with a set of test cases by means of a Monte Carlo simulation and compared to alternative algorithms. It is found that the method improves the accuracy in calculating the collision probability by more than 70% with respect to conventional alternatives. Regarding real-life scenarios, the Cosmos-2251/Iridium-33 and the Chang Zheng-4C/Cosmos-2004 encounters are simulated. In both cases, the time of encounter and collision risk have been correctly estimated with the developed method. Finally, in view of the recent destruction of satellite Cosmos-1408 as a result of an anti-satellite missile test, a screening of its resulting debris threatening the International Space Station (ISS) is performed. During a two-week period, ten close encounters were detected, one of which posed a significant risk to the ISS. When applying the method considering the real shape of the ISS, the collision probability decreases by two orders of magnitude, proving the significance of this approach to correctly estimate the risk and guide space operations.