The Shaykh said:
Whoever is certain about being in a state of Tahārah [purification] and doubts regarding being in a state of Hadath [ritual impurity], he remains in a state of Tahārah. And whoever is certain about being in a state of Hadath [ritual impurity] and doubts whether he is upon Tahārah, he remains in a state of ritual impurity; because the principle [regarding this] is: Al-Yaqīn laa yazūl bish Shakk [Certainty is not removed merely due to doubt] and the foundation is that a thing remains upon that which it was.
This is an important principle and it has numerous subsidiary issues attached to it, and it is founded upon the narration of Abu Hurayrah and Abdullah ibn Zayd (Allāh be pleased with them both) regarding a man who notices something he had in his stomach [i.e. wind] and he was unsure whether something had exited from him or not [passing of wind etc].
The prophet (عليه السلام) said, “do not leave [i.e. the Salāh] unless you hear a sound or notice a smell.” And in the Hadīth of Abu Hurayrah, [the wording of the hadīth is], “Do not leave – meaning the Masjid – unless you hear a sound or notice a smell.”
This Hadith [and the principles extracted from it] resolves many problems and this is from the ease [facilitated] by Islaam, for its goal to remove the Ummah from being in a state of uneasiness, disquiet and confusion, rather it makes affairs explicitly clear. If a person submitted to the likes of these doubts, his life would become difficult, therefore the Legislator, Allāh has cut off these whisperings and doubts.
So as long as these doubts are not proven with certainty, they carry no weight. It is obligatory to repel them and not let them affect you in your [heart and mind], and thus you will be at ease and many problems will be removed from you.
Majmū Fatāwa wa Rasā’il Shaykh al-Uthaymīn Vol.10 Chapter Nullifiers of Wudū