If there's 9000 in the pool I reckon there would be 3000 being paid out on your horse (if there's a third of the pool going to each place getter).
If the horse is paying $3 and $3000 is going out then it seems there must be 1000 winning bets on it or $1000 in bets.
If you add your $50 there will be 1050 bets to share the $3000 between giving a payout of 3000/1050 or about $2.85.

If the horse is paying $1.50 there would be 2000 winning bets so it becomes 2050 with yours making the div 3000/2050 = $1.46

Double the size of the pool and you would half the difference your bet makes.

My logic could be wrong and I worked out the maths on a bit of paper so that probably is wrong, but that's the way I see it.

KV