Try dragging the light blue point on the mirror! Notice that one of the small black vectors is highlighted in red. That red vector corresponds to the path that is dashed and light gray. If the highlighted path is near the path that takes the least amount of time for light to complete, the small black vectors near the highlighted red one all point in more or less the same direction and add together. But if the selected path is far away from the minimum-time path, the vectors there point in completely different directions and cancel each other out.

Reload the page to reset all variables to their original values. Try changing which parts of the mirror are exposed by moving the two cyan points. If you drag one cyan point to around $x = 4$ and the other to $x = 6$, you will notice that the small black arrows point more or less in the same direction. This happens because the minimum-time path reflects off the mirror at $x = 5$. The paths near that center point have only a slight variation in the time light takes to complete them. Since a vector's angle is proportional to the time light takes to complete a specific path, less variation in time means less variation in angle. Because the vectors point mostly in the same direction, their sum is a very long, thick arrow. This means the probability that a photon emitted at A will reach B is very high. Now try moving the two cyan points to $x = 0$ and $x = 2$. The exact same number of vectors now point in very different directions, so the sum of them is way smaller. With that, the probability that a photon emitted at A will reach B is very small too.