Probability Simplex

Let be a finite alphabet. The probability simplex is the set

For example, in with we have:

\begin{document}
\begin{tikzpicture}
 
% Number of subdivisions
\def\N{6}
 
% Coordinates of simplex vertices
\coordinate (A) at (1.3,0);
\coordinate (B) at (0,1.3);
\coordinate (C) at (-0.6,-0.6);
 
% Draw simplex edges
\draw[thick] (A) -- (B) -- (C) -- cycle;
 
% Draw axes
\draw[->] (0,0) -- (1.7,0) node[right] {$P(a)$};
\draw[->] (0,0) -- (0,1.7) node[above] {$P(b)$};
\draw[->] (0,0) -- (-1.0,-1.0) node[left] {$P(c)$};
 
\end{tikzpicture}
 
\end{document}