An integration of distributionally robust risk allocation into sampling-based motion planning algorithms for robots operating in uncertain environments is proposed. We perform non-uniform risk allocation by decomposing the distributionally robust joint risk constraints defined over the entire planning horizon into individual risk constraints given the total risk budget. Specifically, the deterministic tightening defined using the individual risk constraints is leveraged to define our proposed exact risk allocation procedure. Our idea of embedding the risk allocation technique into sampling based motion planning algorithms realises guaranteed conservative, yet increasingly more risk feasible trajectories for efficient state space exploration.