Can confirm, no short lists~
We'll use a Santa's Mega Gift as an example
You have a 12% Chance to strike the "Tier 5-7 Ship" category... a 3% Chance to strike the "Tier 8-9 Ship" category... and a 1% chance to strike the Tier X and Rare Ship" category.
Once you strike a Category, the chance is split across all the available items in the Category. If you have an item already, it will be considered Unavailable. So the chance of getting a specific ship in the Category would be "1/[number of available ships]"