Introducing probability vectors When I studied probability I did it in a classical manner. My course used Loève's book on probability theory and I used Allan Gut's book for a modern version of it. Now I'm following a course in information theory and the notation, terms and concepts change so that it is difficult for me to connect these concepts with what I had. 
I was given the following problem:

What is the minimum value of $H(p)$ as $p$ ranges over the set of
  n-dimensional probability vector.

I looked on Wikipedia and there it says that 

A probability vector or stochastic vector is a vector with
  non-negative entries that add up to one.

My question is how does this concept relates to probability theory. What is a probability vector used for? Is it an extended manner of denoting the probability mass function of a random variable which takes a finite number of values? 

Let $X$ be a random variable with finite support, i.e. the possible values of $X$ are $x_1,\dots,x_n$. Let $p_i=P(X=x_i)$. Strictly speaking, the distribution of $X$ is the measure $\sum_{i=1}^np_i \delta_{x_i}$.
Once you know the support of $X$, in order to describe its distribution, you can just give the vector $(p_1,\dots,p_n)$, which has non-negative entries and adds up to $1$. 
On the other hand, if you choose such a vector, it determines a probability distribution on $\{x_1,\dots,x_n\}$. 
