ClearAll[GetProbability]
GetProbability[{dice1_List, n_Integer}, {dice2_List, m_Integer}] :=
 Module[{a, b, lena, lenb},
  a = Tuples[dice1, n];
  a = Plus @@@ a;
  lena = a // Length;
  a = Tally[a];
  a[[All, 2]] /= lena;

  b = Tuples[dice2, m];
  b = Plus @@@ b;
  lenb = b // Length;
  b = Tally[b];
  b[[All, 2]] /= lenb;

  Total[If[#[[1, 1]] > #[[2, 1]], #[[1, 2]] #[[2, 2]], 0] & /@
    Tuples[{a, b}]]
  ]
GetProbability[{Range[4], 9}, {Range[6], 6}]
GetProbability[{Range[10], 5}, {Range[7], 6}]