After contacting a potential supervisor, is it ok to ask if my application is competitive? I contacted a professor for PhD study, and discussed the project. I would like to make a formal application: should I first ask would it be competitive?
You can ask us but this is a very difficult question to answer for faculty members. 

On the one hand, we don't want to say "yes" and make you feel as though you've been guaranteed a spot when we have no idea of how competitive the pool is this year (see multiple questions/rants on academia.se that reflect just this kind of misinterpretation) --  nor do we want to say "no" and shut you down prematurely. 

So you end up with a qualified "maybe" which doesn't help you (the student) much.