What is the ruling on the prayer of one who had intercourse with his wife, then forgot and only bathed for ablution, and went to the mosque and prayed?

If the wife's truthfulness is highly probable, then ghusl is obligatory, and previous prayers must be redone, because high probability (ghalabat al-dhann) is a basis for rulings, and a man might have intercourse and forget or not be fully awake. However, if the wife's delusion is highly probable, then the ablution and prayers are valid, and nothing is required, because the original state is the acquittal of responsibility (bara'at al-dhimmah). Nevertheless, it is more cautious to act upon her report.