import Data.Ratio
main :: IO ()
main = do
  mapM_ (print . map fromRational . dicePosteriors [4,6,8,12,20])
        [[6], [6,4,8,7,7,2,6], [4,8,7,7,2,6], [6,8,7,7,5,4]]
dicePosteriors :: [Integer] -> [Integer] -> [Ratio Integer]
dicePosteriors suite xxs = f xxs
  where
    f (x:xs) = let zs = foldr p (p x [1,1..]) xs in map (/ sum zs) zs
    f _      = []
    p x priors = zipWith (*) priors $ map (likelihood x) suite
    likelihood :: Integer -> Integer -> Ratio Integer
    likelihood x hypo = if hypo < x then 0 else 1 % hypo