Is it true that ablution does not remove ritual impurity unless one is certain of its occurrence, and that whoever performs ablution while doubtful, then becomes certain of the impurity after prayer, must repeat the prayer and ablution, and that ablution without certainty is not sufficient?

Whoever is certain of purity but doubts impurity, remains in a state of purity. However, if one is certain of impurity but doubts purity, one remains in a state of impurity.

If one performs ablution as a precaution due to doubt about impurity, and then it becomes clear that one was impure before that ablution, the more correct view is that this ablution is not sufficient, because one performed ablution with a wavering intention. Likewise, if someone performs ablution with the intention of renewing it, and then it becomes clear that they were in a state of impurity, their ablution is not sufficient, because they did not intend to remove the impurity, and a recommended act is not sufficient for an obligatory one.