1,2,3 are Prisoners. WB, RG, YC, colors of hats. "RY - W" means if the prisoner sees a Red and Yellow Hat, write White.

The result was generated by enumerating along every possibility of what each prisoner could see. I then took a forced starting point that if 1 saw RY, then W R Y is a win, and B R Y is a loss (a 50/50 split). I then 'stacked' upon the B R Y loss as much as possible (ex. if 2 sees BY, say G, because B R Y is a loss anyway) and sealed the W R Y win (ex. if 2 sees WY, Don't Know). After elimination, make another 50/50 win/lose split and proceed again. I think both losses are forced.

Prisoner 1

RY - W

RC - Don't Know

GY - Don't Know

GC - B

Prisoner 2

WY - Don't Know

WC - R

BY - G

BC - Don't Know

Prisoner 3

WR - Don't Know

WG - Y

BR - C

BG - Don't Know

Result

W R Y - win

W R C - win

W G Y - win

W G C - lose

B R Y - lose

B R C - win

B G Y - win

B G C - win

Chance of being freed = 6/8 = 75% chance.