Each time your horse enters a show, a special counter for that show type is increased.

The sum of all entered shows represents 100%, therefore if you enter an equal amount of shows for each show type, they will have the same % (100%/11)

If you enter only 2 types of shows, you will have 50%/50% on those 2, and 0 on the others. Why would you do that? The higher the % is, the greater the chances of winning in a show of that type.

So if you enter a Racing type and your Racing spec is at 50%, you will have a greater chance of winning than someone whose skill is at 40% (well, it's slightly more complex, but that's the idea).