This paper discusses probability concepts for computing short-term and long-term collision risk that account for correlation effects in geosynchronous orbit (GEO). The focus is on covariance-based methods, which have realistic computer resources requirements. For near-coplanar encounters, a collision probability formulation for position and velocity errors and general orbital motion was developed based on the theory of dynamical probability continua that has been used for debris cloud risk assessment. A method for assessing long-term risk with the purpose of selecting collision avoidance action thresholds on short-term risk is described. This methodology accounts for GEO-specific correlating effects and maintains consistency of uncertainty modeling between short- and long-term risk assessment.