(Uniformly) Random Value when an element is picked with $\frac{1}{p-1}- \frac{1}{(p-1)^2}\ $ probability Let's $\mathbb{F}_p$ be a finite field where $p$ is a large prime number(e.g. 256-bit)

I know if the probability that an element picked from the field is $\frac{1}{p-1}$ we say the element is picked uniformly at random. 

Question: In security context can we say the element is uniformly at random even if its probability is $\frac{1}{p-1}- \frac{1}{(p-1)^2}\ $?
$\mathbb{F}_p$ 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.