Suppose we have a set $X=\{1,...,n\}$ where $n$ is a natural number.
Let $\Delta(X)$ be the set of all probability distributions over $X$.
Then $\Delta(X)$ is a convex set.
How do we interpret convexity in this case? What would be sufficient to show to prove that $\Delta(X)$ is a convex set?
I know that the elements of $\Delta(X)$ satisfy two properties, namely: non-negativity and the sum of all the elements is equal to $1$. But I am unsure how to start proving convexity.