Typical for horses who run the first two legs of the triple crown but who are no longer chasing it: DES MOINES, Iowa -- Paddy O'Prado's co-owner Jerry Crawford told KCCI's Scott Reister that his horse will not run at the Belmont June 5 in New York. Typically, a horse that has run the first two races of the Triple Crown doesn't run the third leg unless he is chasing the Triple Crown. Paddy O'Prado Won't Run Belmont - Sports News Story - KCCI Des Moines