If $X \in \{1, 2, 3\}$, $Y, Z \in \mathbb{R}$ are random variables, what is meant by $X \not\!\perp\!\!\!\perp Y|Z$? Let $X \in \{1, 2, 3\}$, and $Y \in \mathbb{R}$  and $Z \in \mathbb{R}$ denote random variables. Suppose that:
$$X \not\!\perp\!\!\!\perp Y|Z.$$
In words, $X$ is not conditionally independent of $Y$ given $Z$. In probability notation, does the above statement mean one of the following?
(1)
$P(Y|Z, X=1) \neq P(Y|Z, X=2) \neq P(Y|Z, X=3)$
Or does it mean:
(2) $P(Y|Z, X=j) \neq P(Y|Z, X=j')$ for at least one pair of $(j, j')$ where $j \in \{1, 2, 3\}, j' \in \{1, 2, 3\}$ and $j \neq j'$.
Note that (1) is a special case of (2). I'm not quite sure whether $X \not\!\perp\!\!\!\perp Y|Z$ means (1) or (2).

It means (2) to the extent that (2) is well-defined (eg, ignoring concerns about sets of measure zero)
