What are your chances of getting admitted to a competitive school ifyour school does not offer AP or IB programs?

Colleges will look at your course record in the context of your high school, so if your school does not offer any AP or IB programs at all, that typically won't be held against you. What they'll judge you on is whether or not you took the most rigorous schedule available to you; basically, did you take the highest level of course that you were able to take? But they won't hold what your high school doesn't offer against you.

For Ivy league I would say super low but if your school doesnt offer it you have a bit more leeway but not super hopeful as for very prestigious state flagships university in the USA not good but for members of the Association American of Universities Id say a decent shot