Is the prayer valid despite doubt concerning the ablution (wudu'), if one's dominant impression is that it was performed?

Whoever doubts or speculates about his ablution must perform ablution, because the original state is the presence of hadath (ritual impurity), and certainty is not removed by doubt. So, whoever knows he performed ablution and doubts whether he invalidated it or not, he is in a state of purity. And whoever was in a state of hadath and doubts whether he performed ablution or not, he is still in a state of hadath. Overwhelming conjecture is not given consideration unless it is governed by a Shar'i principle. Doubt, according to the jurists, is hesitation between the existence and non-existence of something, whether the two possibilities are equal or one is more likely.