Two ants *A* and *B* are at opposite corners of an 8×8 grid.
Ant *A* starts at the southwest corner and ant *B* at the northeast corner.
Ant *A* moves at a constant speed along the edges of the grid, but can only move to the north
or east. Ant *B* moves at the same speed, but can only move to the south or west. If all pairs
of paths are equally likely, what is the probability that the ants meet? For example, although the
two paths shown below cross, the ants do not actually meet.

Generalize to an *a*×*b* grid.

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