Why didn't the Messenger (peace be upon him) supplicate for his uncle Abu Talib's guidance, even though his prayers were answered?

It is not mentioned in the books of Sunnah that the Prophet (peace be upon him) supplicated for Abu Talib's guidance, despite his eagerness for him to embrace Islam. However, it is reported in Al-Mustadrak of Al-Hakim that he supplicated for his healing, and he was cured. Abu Talib said, "O son of my brother; supplicate to your Lord who sent you to heal me." So the Prophet (peace be upon him) said, "O Allah, heal my uncle," and Abu Talib was cured. Perhaps the Prophet was diverted from supplicating for his guidance due to what was already known in Allah's knowledge and decree: that Abu Talib would not be guided.