A novel second order online local reactive motion planner, named 'Right-of-Way-based Probabilistic Acceleration Velocity Obstacle' (R-PAVO), is developed in this paper in a probabilistic set-up, in which right-of-way rules posed by regulatory authorities are also embedded. The developed motion planning algorithm is capable of generating a collision-free, dynamically feasible and goal-oriented trajectory for each unmanned vehicle (a.k.a. agent) in a multi-agent environment in the presence of uncertainties associated with information on other agents' motion and occluded regions. The considered right-of-way rules facilitate an implicit coordination among the agents that also help in avoiding any reciprocal oscillation in the agents' planned trajectories. Extensive simulation studies are carried out to demonstrate the effectiveness of the developed algorithm in terms of relevant measures of effectiveness indicating real-time implementability of the developed algorithm. © 2022 IEEE.