In Sefer Yehoshua 2:24, the spies tell Yehoshua what they experienced in the land. they say that Hashem has given to us all the land and the people within are afraid.
What a job! They are sent to spy out the land, and see hwo easy it will be to conquer and to get a feel what type of opposition they can expect. They go in and not only do they only go to one city, but they also only go to one house!! Could they really be so confident of the opinion of one person as being truly representative of what everyone else was feeling? Could they really trust one person's opinion and go back and consider this to be the truth, theoretically risking their whole army in the process?
You have to be able to read the signs. They were able to.
As soon as they came in they immediately find out all this information. Clearly it was a sign from Hashem. There wa sno need for them to continue on - Hashem already gave them everything they needed to know. There was no need to waste any mroe time.
It was not specifically what Rahav said, or what they saw the king do. It was everything concentrated together let them realize Hashem was condensing everything for them so they could get back quickly with all the info they needed.
The truth can be hitting you right in the face with clear signs. You might ignore it, or not realize it. or you can open your eyes and see it.