This is probably inanely obvious, but I'm bored. Here is a way to use playing cards to present players with probabilities that have diminishing chances. Get your deck. Take out the jokers. Shuffle. Have your players draw:
Any Number ~70%
Any Heart ~ 25%
A Royal Heart ~6%
The problem is, a deck of cards is more time consuming to shuffle than 7 dominoes. But it's functional. I just stuck with hearts for consistency, but if spades fit your Priest of Dark Fate's petitions better, they would work equally well.
The last probability drops off much faster than the dominoes. You could address this by making the last draw a Red Royal (heart or diamond) which would give you ~ 15%. But I liked the simplicity of going form hearts to hearts.