import Data.Ratio
main :: IO ()
main =
  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 []    _  = []
dicePosteriors _     [] = []
dicePosteriors suite xs = map (/ sum zs) zs
  where
    zs = foldr p [1,1..] xs
    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