= Solution
Use a proper <normal distribution> prior centered at zero on the <log odds ratio>. For example,
$$
\boxed{\beta\sim N(0,1)}
$$
puts approximately 95 percent of its mass between $-2$ and $2$, giving <odds ratios> roughly between $e^{-2}$ and $e^2$, close to $1/8$ and $8$. Centering at zero treats reciprocal <odds ratios> symmetrically. If the desired central 95 percent interval is exactly $(1/8,8)$, use <standard deviation> $\log8/\Phi^{-1}(0.975)\simeq1.0610$. \b[A soft prior is appropriate for implausibility], whereas a bounded <uniform prior> would declare effects outside the limits impossible.
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