Indoor localization has been an active research field for decades, where received signal strength (RSS) fingerprinting based methodology is widely adopted and induces many important localization techniques, such as the recently proposed one building fingerprints database with crowdsourcing. While efforts have been dedicated to improve accuracy and efficiency of localization, performance of the RSS fingerprinting based methodology itself is still unknown in a theoretical perspective. In this paper, we present a general probabilistic model to shed light on a fundamental issue: how good the RSS fingerprinting based indoor localization can achieve? Concretely, we present the probability that a user can be localized in a region with certain size. We reveal the interaction among accuracy, reliability, and the number of measurements in the localization process. Moreover, we present the optimal fingerprints reporting strategy that can achieve the best localization accuracy with given reliability and the number of measurements, which provides a design guideline for the RSS fingerprinting based indoor localization system. Further, we analyze the influence of imperfect database information on the reliability of localization, and find that the impact of imperfect information is still under control with reasonable number of samplings when building the database.