On a grid with corners $(0,0)$ and $(r,k)$, a random walker starts from point $(0,0)$. Each time we flip a fair coin to decide to go to $(x+1,y)$ or $(x,y+1)$, from the point $(x,y)$. The walker is confined to this grid, if it reaches the border and the coin says to pass the border, it does not do anything and flips another coin. We do this until the walker reaches the corner $(r,k)$. For each point $(x_0,y_0)$ on the grid where $x_0,y_0$ are non-negative integers, calculate the probability of the event that walker's distance to the line $y=(k/r)x$ remains less than the distance between point $(x_0,y_0)$ and the same line?
I can calculate the probability that the walker's path contains the point $(x_0,y_0)$, but I don't know how to calculate above.