This study deals with the computation of the instantaneous collision probability between two Earth-orbiting objects of spherical shape. It is expressed as a three-dimensional integral of a Gaussian density on a Euclidean ball of given radius. We propose a new algorithm to efficiently evaluate this integral. This is an extension of a previously studied 3-D method based on Laplace transform and power series evaluation, combined with a new technique using a saddle-point method. A preliminary comparison study with both a Monte-Carlo method and the previous state-of-the-art highlights the potential of this evaluation method, regarding both its efficiency and reliability.