Invisibility works completely when the invisible monster and the detecting monster are far away. When within 5 (or 4?) squares of each other, its location is known to within 1 space (fuzzing the real location by 1 space in all directions). When the invisible monster takes a direct offensive action, or with some probability when it is adjacent, its position becomes known. It still appears as I, but the I will move wherever the monster goes until it becomes 5 or more spaces away, at which point invisibility once again works fully. This could work differently if the invisible monster is stealthy.