Why does the Knight believe the old woman's answer in "The Wife of Bath's Tale"?
We need to remember that when the knight meets the old woman, he is at his wit's end. He has to give the Queen an answer to her question, and, as yet, he has not been able to do so. He is therefore absolutely desperate to find an answer that he can give. In addition, what is interesting about the old woman is the situation in which he finds her. Consider the following description of how they meet. The knight is said to pass a wood:
Where he, all of a sudden, caught a glimpse
Of four-and-twenty ladies in a dance;
And eagerly drew nearer, on the chance
That he would hear of something he could use.
Lo and behold! Before he quite got there,
The dancers vanished, he could not tell where.
Instead of finding the dancers, the only person the knight can see is the old lady who greets him, saying "We old folks know so many things." We can therefore understand why the desperate knight shared his dilemma with the old woman. It is clear that the answer the old woman gave to knight so impressed him with its wisdom and gravitas that he knew instantly that this was the answer he was looking for. Clearly the supernatural surroundings of the old woman points towards her wisdom.