It's calculating distance in 3D space, scaled by the longest distance available. Without the scaling (and ignoring the rounding for the moment), distances from the target to any 3 non-collinear points would narrow it down to at most 2 options, regardless of the precision required on each axis; giving a 50% chance to get it on guess 3 and a 50% chance to get it on guess 4.

With the scaling, it can still be thought of as a problem of intersecting spheres, but the spheres begin to look quite strange since the distance function isn't symmetric. For example if your first guess was a corner of the cube, 1/8 of the space would have the same score (0%) since you've picked the furthest available point. This probably could be analyzed in the same way as above, since the 'spheres' centered at non-corner points aren't degenerate, and their intersections probably still have the right topological dimensions (dropping by 1 each time you add a new sphere, so 3 spheres are still likely to take you to a finite set of points in the continuous case) but that would require some work to prove.

Since we still need to consider the loss of precision from rounding, we can just look at this as a discrete problem and try to find a tuple of points that are sufficient to distinguish everything. It took a me couple of attempts, but the following 4 tetrahedrally arranged ones work: [11,7,4],[4,4,8],[11,8,11],[4,11,7].

There might be a smaller set that work, it would take ~2^48 work to exhaustively search for 3 points that could distinguish everything, and it might be possible to do better since you can choose the second point based on results from the first.