What is the ruling on the prayer of one who doubted the rak'ah during the last prostration of the fourth rak'ah, then inclined to the belief that it was the third, then realized that it was indeed the fourth?

If you are not certain about the Imam's error in missing a رکعة (unit of prayer), then you must follow him. This is because if a worshipper (Ma'mum) is part of a congregation and doubts their own prayer, they should not act on their own doubt but rather follow the Imam. This is what the jurists have stipulated: the worshipper follows their Imam unless they are certain of his error.