Talk about problem but don't talk about your solution in the same domain as your employer while you are with your employer.
Don't discuss the solution with anyone at your workplace or other employees, you are free to talk about the problem and problem space. Don't try to suggest or sell to your employer your solution. Don't use company time and equipment to develop the solution and any associated activities like documentation, presentation, emails or anything to do with your solution. Don't create paper/electronic trail that can date that you came up with solution while you were working with your employer.
Keep developing prototype solution on the side, keep identifying potential buyers, investors, partners etc. (never discuss your solution, just the problem). Focus on learning problem space, key players and solutions in the space. Become expert in problem space inside and outside company. Keep incorporating in your prototype the key problems and features potential buyers indicate. Your prototype need to be a reasonably working solution for B2B buyers to buy.
Once you are reasonably confident about potential of your solution and working prototype, quit your job. Give the impression of you are traveling and relaxing while continue working on your solution for however long your signed agreements, NDA, etc specify (typically 6-12 months is reasonable time after which anything you do belongs to you). Then start your company and go out sell to potential buyer. Avoid having your last employer as first buyer.
Good luck!
ed: IANAL.
I think the first step would be to talk to HR (or if you don't want to do that, take a look at your contract, read it closely, or hire a lawyer) to see what would happen if worst came to worst (if your company took legal action, regardless of if you develop it while working for them, or shortly after quitting).
In my opinion, no. Unless you've cross some proprietary line which would allow them to try to sue you for it anyway, use whatever leverage you feel you have for your own benefit.
Your contract will trump whatever we say, but you say you require knowledge you have because of your employment. That's why your company would (without a contract) be able to claim ownership. The law asks if they gave you the resources to make something.