Rate of dehydration of alcohols having keto group

The other answer by permeakra is sufficient and complete. But, I'd like to add an explanation on how

"A carbonyl group normally destabilizes carbocations but stabilizes carbanions"

For instance, someone can think that the carbocation would resonate with the carbonyl group as what we've learnt earlier, I'd also thought in that way, initially. But, from the following resonance forms,

We can see there is a positive charge on oxygen, which is highly unstable resonance form. So, in this way it destabilizes the intermediate (here carbocation).

Now, one can think what happens when we have a carbanion ;)

A carbonyl group normally destabilizes carbocations but stabilizes carbanions.

In this particular case, the rate of dehydration isn't guarded by carbocation stability, but by CH- acidity. In acidic conditions, OH group in alcohols is relatively easily protonated. Then, if there is a relatively acidic hydrogen in $beta$-position it immediately dissociates, together with a water molecule.

Excercise: Try to draw a mechanism for dehydration of (a) in basic conditions. Hint: it does occur and produces the same product. It does require more heating, though.