A Faraday probe with three concentric rings was designed and fabricated to assess the effect of gap width and collector diameter in a systematic study of the diagnostic ion collection area. The nested Faraday probe consisted of two concentric collector rings and an outer guard ring, which enabled simultaneous current density measurements on the inner and outer collectors. Two versions of the outer collector were fabricated to create gaps of 0.5 and 1.5 mm between the rings. Distribution of current density in the plume of a low-power Hall thruster ion source was measured in azimuthal sweeps at constant radius from 8 to 20 thruster diameters downstream of the exit plane with variation in facility background pressure. A new analytical technique is proposed to account for ions collected in the gap between the Faraday probe collector and guard ring. This method is shown to exhibit excellent agreement between all nested Faraday probe configurations, and to reduce the magnitude of integrated ion beam current to levels consistent with Hall thruster performance analyses. The technique is further studied by varying the guard ring bias potential with a fixed collector bias potential, thereby controlling ion collection in the gap. Results are in agreement with predictions based on the proposed analytical technique. The method is applied to a past study comparing the measured ion current density profiles of two Faraday probe designs. These findings provide new insight into the nature of ion collection in Faraday probe diagnostics, and lead to improved accuracy with a significant reduction in measurement uncertainty.