Pyramid of Probability – Paths and particles

Bob is replacing water molecules with balls in the model. With this stepped pyramid, we can trace the various paths of the balls through it. With each additional level, the paths are split further. The more paths lead into a box, the more balls land in it.
If, however, we only observe a single ball, can we then, prior to the ball passing along the route, make a prediction about the possible path of the ball?