code: def test_prob_t_a_given_s(self):
      # arrange
      src_sentence = ["ich", "esse", "ja", "gern", "räucherschinken"]
      trg_sentence = ["i", "love", "to", "eat", "smoked", "ham"]
      corpus = [AlignedSent(trg_sentence, src_sentence)]
      alignment_info = AlignmentInfo(
          (0, 1, 4, 0, 2, 5, 5),
          [None] + src_sentence,
          ["UNUSED"] + trg_sentence,
          [[3], [1], [4], [], [2], [5, 6]],
      )
  
      distortion_table = defaultdict(
          lambda: defaultdict(
              lambda: defaultdict(lambda: defaultdict(float))
          )
      )
      distortion_table[1][1][5][6] = 0.97  # i -> ich
      distortion_table[2][4][5][6] = 0.97  # love -> gern
      distortion_table[3][0][5][6] = 0.97  # to -> NULL
      distortion_table[4][2][5][6] = 0.97  # eat -> esse
      distortion_table[5][5][5][6] = 0.97  # smoked -> räucherschinken
      distortion_table[6][5][5][6] = 0.97  # ham -> räucherschinken
  
      translation_table = defaultdict(lambda: defaultdict(float))
      translation_table["i"]["ich"] = 0.98
      translation_table["love"]["gern"] = 0.98
      translation_table["to"][None] = 0.98
      translation_table["eat"]["esse"] = 0.98
      translation_table["smoked"]["räucherschinken"] = 0.98
      translation_table["ham"]["räucherschinken"] = 0.98
  
      fertility_table = defaultdict(lambda: defaultdict(float))
      fertility_table[1]["ich"] = 0.99
      fertility_table[1]["esse"] = 0.99
      fertility_table[0]["ja"] = 0.99
      fertility_table[1]["gern"] = 0.99
      fertility_table[2]["räucherschinken"] = 0.999
      fertility_table[1][None] = 0.99
  
      probabilities = {
          "p1": 0.167,
          "translation_table": translation_table,
          "distortion_table": distortion_table,
          "fertility_table": fertility_table,
          "alignment_table": None,
      }
  
      model3 = IBMModel3(corpus, 0, probabilities)
  
      # act
      probability = model3.prob_t_a_given_s(alignment_info)
  
      # assert
      null_generation = 5 * pow(0.167, 1) * pow(0.833, 4)
      fertility = 1 * 0.99 * 1 * 0.99 * 1 * 0.99 * 1 * 0.99 * 2 * 0.999
      lexical_translation = 0.98 * 0.98 * 0.98 * 0.98 * 0.98 * 0.98
      distortion = 0.97 * 0.97 * 0.97 * 0.97 * 0.97 * 0.97
      expected_probability = (
          null_generation * fertility * lexical_translation * distortion
      )
      self.assertEqual(
          round(probability, 4), round(expected_probability, 4)
      )
  
file_path: nltk/nltk/test/unit/translate/test_ibm3.py
imports: import unittest
  from collections import defaultdict
  from nltk.translate import AlignedSent, IBMModel, IBMModel3
  from nltk.translate.ibm_model import AlignmentInfo
label_desc: Use image node_id 3 for calling the TestIBMModel3 obj's underlying member method code with example usage: obj.test_prob_t_a_given_s() without return types