Your initial assumption was correct. The best place to find this information is to look at the "Help" tab in the top right corner.
When a game has multiple types of cards included, game creators can control how common each type is by defining different weights.
Weights are relative to eachother. That is, if all cards have the same weight, they will be equally likely. If a card's weight is double that of another card, that card will show up twice as often as the other.
If a weight is not listed next to a card on the settings panel, it is assumed to be the default of 1.
A card with a weight of 0 will never be randomly awarded and can only be acquired via minimums.