KöMaL 2023 C1757

Johnny got a robot for Christmas, and he is trying it on a square carpet. The length of the sides of the square is $4$ metres, and its vertices are $A$, $B$, $C$ and $D$, in this order. Let $P$ denote the interior point of square $ABCD$ which is exactly $1$ metre away from both of sides $AB$ and $BC$. The robot is initially standing at point $P$, and starts to move in a random direction. When it has covered $2$ metres, it will stop. What is the probability that the robot will get off the carpet?