Existing old reinforced concrete buildings could be vulnerable to earthquakes because they were constructed without satisfying seismic design and detail requirements. In current seismic design standards, the target collapse probability for a given Maximum Considered Earthquake (MCE) ground-shaking hazard is defined as 10% for ordinary buildings. This study aims to estimate the collapse probabilities of a three-story, old, reinforced concrete building designed by only considering gravity loads. Four different seismic design categories (SDC), A, B, C, and D, are considered. This study reveals that the RC building located in the SDC A region satisfies the target collapse probability. However, buildings located in SDC B, C, and D regions do not meet the target collapse probability. Since the degree of exceedance of the target probability increases with an increase in the SDC level, it is imminent to retrofit non-ductile RC buildings similar to the model building. It can be confirmed that repair and reinforcement of old reinforced concrete buildings are required.