An urban water supply network (WSN) is a crucial lifeline system that helps to maintain the normal functioning of modern society. However, the hydraulic analysis of a significantly damaged WSN that suffers from pipe breaks or leaks remains challenging. In this paper, a probability-based framework is proposed to assess the functionality of WSNs in the aftermath of powerful earthquakes. The serviceability of the WSN is quantified by using a comprehensive index that considers nodal water flow and nodal pressure. This index includes a coefficient that reflects the relative importance of these two parameters. The demand reduction (DR) method, which reduces the water flow of nodes while preventing the negative pressure of nodes, is proposed. The difference between the negative pressure elimination (NPE) method and the DR method is discussed by using the example of a WSN in a medium-sized city in China. The functionality values of the WSN are 0.76 and 0.99 when nodal pressure and nodal demands are used respectively as the index of system serviceability at an intensity level that would pertain to an earthquake considered to occur at a maximum level. When the intensity of ground motion is as high as 0.4 g, the DR method requires fewer samples than the NPE method to obtain accurate results. The NPE method eliminates most of the pipes, which may be unrealistic.