How is a horse race purse split between the horses?

This depends on the track and on how far down the ranks the track is paying.

"Generally, first place gets 60% second 20% third 10% fourth 5% with the remaining 5% paying out to some portion of the rest of the field.

Some states/tracks pay every horse in the race a set amount...say 350 dollars, which encourages more starters.

In some races the money to pay the field comes from the winning horse's part of the purse in others it is taken from the purse "up front" with the remainder

split between places 1-3, 1-5 depending on the condition book or on decisions made for a specific race meet, day of week.