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"]
      src_classes = {
          "räucherschinken": 0,
          "ja": 1,
          "ich": 2,
          "esse": 3,
          "gern": 4,
      }
      trg_classes = {
          "ham": 0,
          "smoked": 1,
          "i": 3,
          "love": 4,
          "to": 2,
          "eat": 4,
      }
      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]],
      )
  
      head_distortion_table = defaultdict(
          lambda: defaultdict(lambda: defaultdict(float))
      )
      head_distortion_table[1][None][3] = 0.97  # None, i
      head_distortion_table[3][2][4] = 0.97  # ich, eat
      head_distortion_table[-2][3][4] = 0.97  # esse, love
      head_distortion_table[3][4][1] = 0.97  # gern, smoked
  
      non_head_distortion_table = defaultdict(
          lambda: defaultdict(float)
      )
      non_head_distortion_table[1][0] = 0.96  # ham
  
      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,
          "head_distortion_table": head_distortion_table,
          "non_head_distortion_table": non_head_distortion_table,
          "fertility_table": fertility_table,
          "alignment_table": None,
      }
  
      model4 = IBMModel4(
          corpus, 0, src_classes, trg_classes, probabilities
      )
  
      # act
      probability = model4.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 * 1 * 0.97 * 0.97 * 0.96
      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_ibm4.py
imports: import unittest
  from collections import defaultdict
  from nltk.translate import AlignedSent, IBMModel, IBMModel4
  from nltk.translate.ibm_model import AlignmentInfo
label_desc: Use image node_id 3 for calling the TestIBMModel4 obj's underlying member method code with example usage: obj.test_prob_t_a_given_s() without return types