Maintaining a belief instead of a single guess
Probabilistic localization replaces the idea of a single tracked coordinate with a belief: a probability distribution over every position the robot might plausibly occupy, weighted by how consistent each position is with everything sensed so far. Early on, or right after something goes wrong, that belief might be spread wide, the robot genuinely isn't sure where it is among many candidates. As consistent evidence accumulates, the belief concentrates around the positions that keep matching what the robot senses.
Localization, under this framing, isn't a single calculation, it's a continuous process of updating this belief as new information arrives. The robot never declares 'I am definitely here,' it instead reports something closer to 'I am most likely here, and here's how confident I am, based on everything so far.'