From the wording of your question, I get the impression that you don't actually understand what a cumulative distribution function is. In your case, it says "If my X process follows a Weibull distribution which has parameters alpha, beta, and gamma, what is the probability of getting an outcome less than or equal to a particular value x?" The values of alpha, beta, gamma, and x are all inputs to the function, and the output is a probability.
If you have observations of a real-world process you are trying to model, you can try to estimate the parameters based on your data using a variety of distribution fitting techniques.