Rules for mystery skins: https://support.riotgames.com/hc/en-us/articles/201752934-Mystery-Gifting-FAQ
Ultimate probability generic calc:
S = # of skins > 520 RP for the champs you own
U = # of ultimate skins for the champs you own
O = # of skins you already have
Assuming you don't own any ultimate skins, chances of getting one from a mystery gift look like:
U / (S-O)
If you wanted to boost your chances, you could do the following:
Get a new account.
Only buy champs with ultimate skins (Ezreal, Udyr, Sona)
You should have more than 10 available skins depending on what limited ones are in the store, so you should be eligible for mystery gifts. Ez has 8 skins, Sona 6, Udyr 3, so you're good.
Assuming all of those skins are available in the store, math looks like:
3 / 17 or ~17% chance of getting an ultimate skin. So 490 RP * 6 tries = 2940 rp on average to get an Ultimate. Cheaper than the 3250 rp for an ultimate!