How do I see the following fact?

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> If $R$ has dimension $1$, and $a$ is a non-zerodivisor and non-unit, then $R/(a)$ has dimension $0$. 
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That is saying if $P\_1\supset P\_2\supset (a)$ are two prime ideals, then $P\_1 = P\_2$, i.e all prime ideals over $(a)$ are maximal.