Part 2 - To bet a certain amount on a race.
The formula is -

m = 100/p

where p is the sum of the percentage chance of each selection.

Example.
Again we have 2 horses - horse (a) paying $5 and horse (b) paying $10. So the percentage chances of each horse is 20% for (a) and 10% for (b). The sum of the percentage chance, the value of p in the formula, is 30.

m = 100/30
m = 3.33

Now we multiply each percentage chance by m -
(a) = 20 * 3.33
(b) = 10 * 3.33

(a) = $66.60
(b) = $33.30

Total bet on the race is roughly $100
If you only wanted to bet $25 on the race you would multiply the amounts above by 25/100. So (a) would become 0.25 * 66.6 = 16.65 and (b) would become 0.25 * 33.3 = 8.33 which gives us a total around $25

I hope this helps you out and helps you make a profit or more of a profit.