KöMaL 2018 C1489

In the lower left corner of a chessboard there is a black bishop, and in the lower right corner there is a white bishop. Each bishop moves up the board in steps of one unit, remaining on fields of its own colour. In each step, it may move to the left or to the right, at random, until it reaches the top row. What is the probability that the black bishop ends up to the right of the white bishop?