I think that it depends on the product but I know really a lot of examples when a small app actually not just pays its hosting bills but bring a lot of revenue.
I'm myself working on http://pingr.io and struggling to find customers. But gosh, how many products like currency converter or something exist which have a lot of users and revenue.
My points:
1. If your project is useful for people some of them will use it
2. It doesn't matter if free versions exists. People by coffee in stores (cheap) and in Starbucks (expensive). People order taxi (paid), when they can use autobus (might be free or very cheap).
3. But your product should be a bit better or at least the same as others
4. Now, one crucial moment is pricing. Once I posted my product on reddit and was surprised that people started comparing my pricing to competitors, and they were complaining about it. But still. I know a guy whose prices are literally x3-x5 higher than others, while his app is not that good, and he still has ~$4000 revenue per month
BUT
Keep in mind, that if you're not going into "business way" meaning instantly paying ads/watching conversions/investing/taking risks etc, it may take a LONG time (1-3 years) to get exposure
In a nutshell: just make a good app, put pricing (average among competitors) and start talking about it everywhere for a year. If the app is good, it'll bring you money (at least there is probability)