Chemistry - Rate of dehydration of alcohols having keto group
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.