What exception must be made if $|a|=|b|=1$ to $|\frac{a-b}{1-\bar{a}b}|=1$

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The problem is :

Prove that $$|\frac{a-b}{1-\bar{a}b}|=1$$ if either $|a|=1$ or $|b|=1$. What exception must be made if $|a|=|b|=1$.(where $a$, $b$ are both complex number and $|1-\bar{a}b|\neq 1$)

I can proof $$|\frac{a-b}{1-\bar{a}b}|=1$$ if either $|a|=1$ or $|b|=1$. But I do not understand the request What exception must be made if $|a|=|b|=1$.