Hmm, if I do it manually I come up with another figure:
.75 first choice is non-green
Assuming first choice is non-green, then probability of second choice being white is…
1/3 if first choice was either blue or red (2 possibilities)
0% if first choice was white (1 possibility)
(1/3 + 1/3 + 0)/3 = 2/9
.75 * 2/9 = 1/6