Why do we take a probabilistic approach to model the world for robots in occupancy grid maps?

Probabilistic approach is not only used in occupancy grid maps but also used in most of the mobile and aerial robots problems, it is a branch of robotics

It is commonly used in robots that can move or fly rather than robots that do not leave its initial position like robotic arms.

Uncertainties come from sensors and mathematical models as well. They can build up and lead to catastrophic consequences, So probabilistic approaches seek to filter out these uncertainties to develop a good environment perception.

Occupancy grid mapping is a subset problem that is handled by the probabilistic approaches. These approaches are used in occupancy grid to investigate the occupancy state of the space ahead using noisy sensor observations and noisy motion models.

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