Change a cell in a range and all other cells in the range change to keep the sum at 100%

This pertains to a league team payout structure.

There can be up to 24 teams. The teams place from 1st through 24th in the final standings. Each team gets a percentage of the overall league payout based on their final place in the standings. I want the last place team (no matter how many teams are in the league for a given season) to automatically populate the correlating % cell (D30 in the example) with a percentage that makes the team payout for last place always be $180.00 and make all other team's (above last place) pay out percentage change automatically with a sliding scale that is weighted slightly heavier towards the top.

I've attached an example of what I'm doing. In the example there are 9 teams of a possible 24.

Basically, I'd like to be able to change any of the cells in Range (D22:D45) to any number from 1 to 100 and have all of the other cells in the range automatically recalculate themselves and changing their values so the SUM of the range is always 100%. There needs to also be a way to deal with teams that have a tie in number of games won....

I appreciate any help you can provide. Thanks!