If we are given two distributions, $P_1$ and $P_2$ over the same measure set $(X,E)$, where $X$ is the domain and $E$ is a collection of subsets of $X$. Then total variance between $P_1$ and $P_2$ are defined as,
$$ V(P_1,V_2) = \sup_{e \in E} |P_1(e) - P_2(e)| $$
As I can understand this, it measures the longest distance between the distributions for the same set of points. For a demonstrating example, if $E = {1,2,3}$ and $P_1(1) = P_1(2) = P_1(3) = \frac{1}{3}$, and $P_2(1) = P_2(2) = \frac{1}{4}, P_2(3) =\frac{1}{2}$, then $V(P_1,P_2) = |\frac{1}{2} - \frac{1}{3}|$.
Is this correct ?