Bots on grid - Colegiul National C. Negruzzi (Iași - Roumanie)

Given a (x, y, z) three-dimensional grid and two different bots moving one unit per step, towards the opposite corner, at the same pace, starting at the same time, from points (0, 0, 0) and (x, y, z) , we try to find the chances of the two bots meeting on one of the grid’s points.