Successful integer estimation of carrier phase ambiguities of Global Navigation Satellite Systems (GNSS) is the key to many high precision positioning applications. In order to describe the quality of the positioning results rigorously, one needs to know the probabilistic properties of both the integer and noninteger parameters in the GNSS model. In this contribution these probability distributions are presented and discussed. The probability mass function of the integer ambiguities is needed to evaluate the ambiguity success rate and the distribution of the GNSS baseline is needed to evaluate the relevant confidence regions for positioning.