Kalman Filter | Why Shift the Belief Distribution
The idea is that the robot is trying to figure out where it is.  The only information it can use is:


Its door sensor which says either you're next to a door or you're not next to a door.
Its map of where the doors are.


That's how we go from the "maximum confusion" (uniform) plot to the one with three humps. This uses the first you're next to a door measurement.

Then, the robot knows it moves to the right.  Therefore it must update its probability with a similar movement to the right.  However, its motion sensors are a little uncertain, so this has the effect of smoothing the three bumps (well, the whole distribution) a little bit. So the three bumps move to the right and they spread out a little.

The peaks of the three spread out humps are still the robot's best guess as to where it is on its map.

Now we get the second you're next to a door measurement.  We multiply our prior (the slightly spread out three-humped distribution) with a new three humped distribution (from our known map).  The prior second-door location and the map second-door location will align, so that will generate the largest peak.