Let $\mathfrak{M}_{\mathbb{Q}}$ be the set of places of $\mathbb{Q}$, where the corresponding absolute values are normalized in the standard way. Then $(\mathbb{Q},\mathfrak{M}_{\mathbb{Q}})$ is an adelic field that satisfies the product formula. If $\mathbb{K}$ is a number field, by the construction above, we obtain an adelic field $(\mathbb{K},\mathfrak{M}_{\mathbb{K}})$ which satisfies the product formula too.