Clearly you need a "Competitor" table if you wish to represent them, which I assume you do! This would connect to the "Races" table (though personally I would call this "Division"). I would assume the existence of the competitor linked to a Race would represent an entry.
Personally I would create a new table called "Discipline Type" which would differ from "Race Type". The two are functionally independent - race type could be "Triathlon" while "Discipline Type" could be "Swimming"/"Running"/"Road Cycling".