Negligible functions in definitions of statistical closeness and computational indistinguishability
Statistical distance between $X_n$ and $Y_n$ can be defined as the maximum, over all functions $D$, of
$$ |P(D(X_n) = 1) - P(D(Y_n) = 1)|. $$

In particular, if the statistical distance between two sequences of distributions $\{X_i\}_{i \in \mathbb{N}}$ and $\{Y_i\}_{i \in \mathbb{N}}$ is negligible (eventually smaller than $1/p(n)$ for any polynomial $n$) then they are computationally indistinguishable.
The other direction is not true, and this is what drives all of cryptography.

I leave it an exercise to show that if two sequences distributions have zero statistical distance (i.e., they are copies of the same random variables) then they are computationally indistinguishable.