Is there conditional independence when one conditioning variable is the linear combination of another?

Question

Conditional independence of random variable $Y$ of $Z$ conditional $X$ is defined as

$$P(Y|X,Z) = P(Y|X)$$

Does this relation hold for any continuous $X$ and $Z$ if $Z = a + bX$, where $a$ and $b$ constants in $\mathbb{R}$? If not, does it hold under specific assumptions?

Edit: A relevant extension of my question is, what about the reverse situation:

$$P(Y|X,Z) = P(Y|Z)?$$

Answer 1

It will always hold if $Z=f(X)$, i.e. if $Z$ is known given $X$. Apart from that then it depends on $Y$. For example $Y$ independent of $Z$ would work regardless of the relationship between $X$ and $Z$.