Is there notation for '$x$, where $x$ has an equal probability of being $1$, $2$ or $3$'?

Question

Basically the question is in the title, something like '$x$, where $x = [1(1/3), 2[1/3], 3[1/3]]$'.

Guess it could be notated as a random integer between $1$ and $3$, if notation exists for that.

This is for an art installation not a mathematics paper, so apologies if the question seems dumb but I want to use existing notation if it exists. :)

Answer 1

Such a variable has a discrete uniform distribution, so you may write $X\sim \mathcal{U}\{1,\,3\}$ (random variables are usually capitalised).

Answer 2

There is the notation $X\sim_\Bbb P\mathcal{U}(S)$ to indicate that $X$ follows the uniform distribution on a set $S$. In you case this would give $$X\sim_\Bbb P\mathcal{U}(\{1,2,3\})$$ Some would also write $$X\sim_\Bbb P\mathcal{U}\{1,3\}$$ as indicated in this wikipedia page.