Here, we describe a three-dimensional (3-D) current mapping technology developed for a superconductor using an array of Hall sensors distributed around it. We demonstrate this in a prototype similar to a conventional resistive superconducting fault current limiter (SCFCL). By calibrating the Hall sensor voltage, we can directly measure the distribution of the currents in the superconductor and the shunt. Using pulsed measurements, we measure the fractions of current distributed between the superconductor and shunt resistor parallel combination when a fault-like condition is mimicked in the system. Using the Hall array measurements, we generate a real-time 3-D map of local average current distribution around the superconductor used in our prototype of SCFCL. Our measurements show that even for currents less than the critical current a nonuniform current flow pattern exists around the superconductor, which we have used in the prototype. The capability of real-time, 3-D monitoring of the average local current distribution offers a way for the early detection of instabilities like hotspots developing in a superconductor. We discuss the use of this technique to not only show how it offers early detection and protection against instabilities developing in the superconductor, but also how it offers an added flexibility, namely, a user-settable fault current threshold.