Both toprut buys the applicant database and runs draw simulations on the data, I believe gohunt does the same. But again, you need to remember that those are last years odds. If the apps stay pretty much the same for the coming year, so will your odds.
If you're wondering how or why toprut does his nm odds, email him. He's easy to talk to and pretty upfront with his methods.
from my notes...
the correct way to figure is to calculate your chance of not drawing any tag at all, then take the inverse as your odds of drawing at least one of the tags.
For example you have a 25/26 (or 96.15%) chance of NOT drawing a deer tag, a 433/434 (or 99.77%) chance of NO elk tag, etc,etc,
Multiply all .9615 x .9977 x .9991 x .75 = .7188 or a 71.88% chance of not drawing any tag, with the inverse (100% minus 71.88%) being 28.12% chance of drawing at least one tag.