Sax already won the game as Max begs Rex to tell him the identity of the person who has lost the draw. "If Fax won a prize, give me Sax's name. If Sax won a prize, give me Fax's name.
so actually that left only Fax and Max
Sax is happy about it when Max tell him the result is because he has already won the lottery
so the lottery is now between Fax and Max only
their chances went up from 1/3 to 1/2 because there is only 2 person left.