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According to Wikipedia, the parameter in a Bernoulli distribution should be $0<p<1$.

I am reading this famous paper proposing Hierarchical Dirichlet Process, and on page 1580, A.6 and the sentence right after it, they state

$$q(s_j|\alpha_0)\propto\Bigg(\frac{n_{j..}}{\alpha_0}\Bigg)^{s_j}$$

but $n_{j..}$ is an integer which can take any large value, while $\alpha_0$ is a real value which almost always is way below $n_{j..}$. Also $s_j$ is a binary value either 0, or 1.

How can I convert it to an actual Bernoulli?