How is artificial; selection dependent on variation in nature?

Artificial selection is the breeding of the best species by humans. For example, the fastest horse or something like that. This means breeding with species with the traits that produce offspring with the desired traits. To do this variation is needed. Not all species are going to have the desired traits but not all are going to have the undesired traits. However, if there is no variation, all animals of the same species are either going to have the unwanted traits or the desired traits. Now, if they all have the traits that us, humans, don't want, then such a concept and process like artificial selection would not exist.