Having internal mental experiences causes my brain to send physical signals to my fingers in order to type the words "I have internal mental experiences". A philosophical zombie would type those same words, but they would be caused by something else since by definition it lacks those experiences. That would be rather surprising, and it would be even more surprising that the words that the zombie emits coincidentally correspond exactly to the experiences that the non-zombie has.
(See https://www.lesswrong.com/posts/fdEWWr8St59bXLbQr/zombies-zo... for a much longer version of this argument)