(Uniformly) Random Value when an element is picked with $\frac{1}{p-1}- \frac{1}{(p-1)^2}\ $ probability
$\mathbb{F}_p$ actually has p elements. Hence, an element would be picked uniformly at random if every element was chosen with probability $1/p$. Already if one element is chosen with probability $\frac{1}{p-1}$ this is not a uniform distribution anymore. Depending on the size of $p$ you can argue that the distribution is statistically indistinguishable from a uniformly random one.