Conflict method is regarded as a viable solution for the drawbacks in the gap-acceptance approach. It has been used for the capacity analysis of unsignalized intersections, which includes the two-way stop-controlled, and the all-way stop-controlled types. This method is now applied for the capacity estimation of vehicular streams at a non-priority intersection, where gap-forcing, poor lane discipline, violation of priority rule, and heterogeneous traffic co-exist. However, there are some issues encountered when applying the conflict method for non-priority intersection analysis, particularly with the occupation time and heterogeneous traffic. The concepts developed for capacity estimation have considered the blocking effect from all possible conflicting streams. Therefore, the additional concept with volume portion, P n,i is introduced. The probability of non-blocking traffic streams and the portion of consumed shared capacity by the subject stream are analyzed. The portion concept, P n,i provided a more realistic estimation. The proposed approaches generated high capacity values, even though the observed intersections have near-saturation traffic. A high percentage of small vehicles occupied the lateral lane space, which is permitted by gap-forcing and poor lane discipline, apart from their smaller footprint.