Representation of the dual of $C_b(X)$?

On a metric space $X$, Did said:

the space $M_1$ of probability measures is included in the dual of the space $C_b$ of bounded continuous functions.

I was wondering what is the representation theorem for the dual of $C_b(X)$, which is supposed to have $M_1$ as its subset?

I saw in Wikipedia, only Riesz representation theorems for $C_0$ and $C_c$, not for $C_b$.

Thanks and regards!

For the sake of having an answer to the question, Martin's comment contains the key point. We have an isomorphism $C_b(X) \cong C(\beta X)$ where $\beta X$ is the Stone-Čech compactification (defined for arbitrary topological spaces; some authors put extra conditions on $X$ but these are just the conditions required for the natural map $X \to \beta X$ to be an embedding), so by the ordinary Riesz representation theorem describes the dual of $C_b(X)$ in terms of measures on $\beta X$.