Probability of Attaining the/a Global Optimum
No, you can't infer that.  You seem to be assuming that the optimization process tries one element of the search space, chosen uniformly at random, and hopes that it got lucky.  But that's not how real optimization algorithms work.  They try multiple solutions, and they're not chosen uniformly at random; they're typically chosen in some way that we hope is more likely to hit a good solution.
In general, you cannot conclude anything about the probability of hitting the optimum after some amount of optimization, without further information.  The probability might be much larger than $N/|S|$ (e.g., if the optimization problem is easy or the optimization algorithm is effective on this kind of problem).
In the kinds of optimization problems we typically use a computer to solve, often you can't just &quot;plot it out&quot; as often we're working with a multidimensional search space.