First, the answer is that the callable bond’s effective duration will lengthen, not the straight bond’s.
Second, the key bits of information that you omitted were that the coupons on all three bonds are 4% while the YTM is 2.5%.
Under those circumstances, the straight bond’s effective (and modified) duration will shorten as the YTM rises, and the putable bond, with its option out of the money, will behave like the straight bond. The callable bond, on the other hand, has its option in the money, but moving out of the money as interest rates rise. It’s in the region where it has negative convexity, so as the YTM rises, its effective duration lengthens.
The details are important here.