Let me illustrate a probable story which might muddy the waters and expand the surface area of belief.
Consider a woman whose child is suffering from a disease. She has gone to all the doctors she was recommended and found no success. She is told to visit Church and pray to Jesus. After the sunday mass, she tells her story to few random church goers. They immediately recognize the medical condition and tell her to visit a particular doctor. Doctor sees her child and provides medication. Her child is cured after few years. Now the question is did she know going to church would solve her medical problems?
That one is clear to me too, also no. How would she know? No where did you specify that she even thought going to church would solve her problems. She was told to visit church, yes, but there has to be a belief component to "knowing". Did she genuinely believe going to church would solve her medical problems? Hope and desperation don't count either, it has to be a genuine belief. Also, she was told be pray to Jesus. Depending on if you're religious or not you might say that Jesus did cure her, but a pretty strong argument could be made that the church-goers were the key, so even if she did believe Jesus would cure her, if it ends up being something else, then it also doesn't count.
There is clear chain of links : Belief (Jesus solves problems) -> Action (Going to church) -> Finding solution (Other church goers helped her). How is this different than original gettier problem? In original gettier problem, his problem was solved in unexpected ways.
As I see it, there are four quadrants : 2 (action, no action) x 2 (solution, no solution). You can build any story based on outcomes.
Consider a woman whose child is suffering from a disease. She has gone to all the doctors she was recommended and found no success. She is told to visit Church and pray to Jesus. After the sunday mass, she tells her story to few random church goers. They immediately recognize the medical condition and tell her to visit a particular doctor. Doctor sees her child and provides medication. Her child is cured after few years. Now the question is did she know going to church would solve her medical problems?