Is a woman considered irrevocably divorced after being divorced three times at once, and then the judge affirmed the divorce and annulled the contract due to the husband's failure to appear in court, or is it considered two divorces and he has the right to take her back?

The questioner did not mention the wording of the divorce, but if he said, "You are divorced, you are divorced, you are divorced": If he intended three divorces: his wife is irrevocably divorced from him according to the majority of scholars, and she is not lawful for him until she marries another husband (this is contrary to Sheikh al-Islam, who considers it one divorce). If he intended one divorce repeated for emphasis: then it is one divorce.

If the judge ruled a second divorce: If the husband had taken her back after the first divorce: it is a second divorce, and he may conclude a new marriage contract with her after her waiting period ends. If he did not take her back and her waiting period ended: she is irrevocably divorced from him with a minor irrevocable divorce, and the judge's divorce has no bearing.