The bank case:
On Friday, a man and his wife go to the bank and see a long line. The man says “Oh well we can go tomorrow” and asked how he knows, he says “I was here last Saturday and they were open.”
Alternate scenario, it’s really impt that they deposit their check. He is asked “how do you really know? Maybe they changed their hours.” and he updates “You know, you’re right, I don’t know.”
Contextualist wants to say “I know X” and “I don’t know X” were both truthful utterances with no change in world state (but rather, what changed was the context-dependent truth conditions)
Epistemological contextualists claim that the standard for knowing X is dependent on what doubts have been raised in a conversation (the doubts become ‘live’). Skepticism is addressed because we can hand the skeptic a victory in their ivory tower (you are right that we don’t know anything) while denying the skeptic the right to challenge an ordinary person living their life claiming to know many things.
Counterpoint: why were hyperbolic doubts even raised? Actually, the skeptics were concerned with ordinary claims of knowing.
Contextualists could be said to be using some motivated reasoning to insulate ordinary belief from what goes on in the phil seminar room.