For the third hole do not drill all the way into the second plate, just enough to go about half way through or less. The diameter of the holes should be just under the diameter of the balls so that they won't get wedged into the holes when clamped together.
Now unclamp the plates and through the partially drilled last hole finish drilling a hole the same size as the drill bit you will be using to drill your hole in the ball.
Place three balls in the holes and clamp the plates together and line them up on your drill press table with the drill bit.
Use plenty of lubricant and every fraction of an inch you go down lift the bit a little to clear chips and allow more lube to enter.
That's it. Very simple, very easy. Works very well for me.