Generate uniformly distributed random numbers between [a b] which occur with probablity c uniformly?

I want to generate random number between [a b] which is uniformly distributed and occur with probability of c uniformly.

I have one approach

x = rand(1,n);
y = zeros(1,n);
    for i = 1:n
        if x(i) > 1-c
            y(i) = rand()*(b-a)+a;
        end 
    end

But I am not sure whether it is correct or not.