In a communication-constrained and adversarial environment, it is an interesting and challenging problem for multiple vehicles to patrol the whole environment by sensing with their limited visibility. Early works based on deterministic paths are predictable to the adversary, and recent non-deterministic works are limited to only a circular environment and require synchronization. So, we propose a method of finding patrolling policies for multiple vehicles that monitor any polygonal environment using limited visibility regions and non-deterministic patrolling paths. First, limited visibility regions are calculated for a subset of locations that cover the whole environment or a part of the environment. Then, we find distributed patrolling policies in the form of Markov chains, using convex optimization to minimize the average expected commute time for the subset of the locations permitting each vehicle to cover the whole environment independently. We also find coordinated and Markov chain based patrolling policies that minimize the average commute time for the subset of locations permitting each vehicle to cover a part of the environment and additionally, communicate with a centralized base station. We present multiple simulation results to show the effectiveness of our visibility-based non-deterministic patrolling method.