We've al had solutions for problems that don't exist. Well. I have. How do you test if those solutions are not just for you, but for many people. How do you know if an idea is worth building?
Try to build a prototype, aiming on MVP, make it publicly available and then distribute it to the people around you and online using the social networks. Using the feedbacks, you'll know if it's worth continuing or just dropping the project and switch on another idea :)
the best and easy way to know it it works for a lot of people is asking people that may use it. That's the fastest way to validate an idea of a startup, business, etc.
I work with a lot of startups and serial entrepreneurs who use this method to discover what might be profitable:
It's like fishing, each website you put online is like having another hook in the water. You don't know which one is going to get the bites :D The key thing is don't invest too much time or money before you know you have any bites. Once an idea looks profitable, that's when you begin building your MVP. This way you're not investing time and money into a dead-end.
Cliff Rowley
Thinker, Tinkererer, Dork.
This is the million dollar question ;-)
In my experience..
And then some more belief and luck wouldn't go amiss.
Edit: in fact, I feel should elaborate a little more. @deviantony's suggestion of building a minimum viable product is a must whether you believe whole heartedly that the idea will be a hit or whether you just don't know. Building an MVP not only allows you to get the idea out there in the wild and to see how your potential users react - but it also allows you to put a cap on the amount of time and effort you put into an idea that isn't a hit.