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In an environment with certain locations of higher priority, it is required to patrol these locations as frequently as possible due to their importance. However, the Non-Priority locations are often neglected during the task. It is necessary to balance the patrols on both kinds of sites to avoid breaches in security. We present a distributed online algorithm that assigns the routes to agents that ensures a finite time visit to the Non-Priority locations along with Priority Patrolling. The proposed algorithm generates offline patrol routes (Rabbit Walks) with three segments (Hops) to explore non-priority locations. The generated number of offline walks depends exponentially on a parameter introduced in the proposed algorithm, thereby facilitating the scalable implementation based on the onboard resources available on each patrolling robot. A systematic performance evaluation through simulations and experimental results validates the proportionately balanced visits and suggests the proposed algorithm's versatile applicability in the implementation of deterministic and non-deterministic scenarios.