The main contribution of this paper is a strong converse result for K-hop distributed hypothesis testing against independence with multiple (intermediate) decision centers under a Markov condition. Our result shows that the set of type-II error exponents that can simultaneously be achieved at all the terminals does not depend on the maximum permissible type-I error probabilities. Our strong converse proof is based on a change of measure argument and on the asymptotic proof of specific Markov chains. This proof method seems to be useful also in other applications, and is appealing because it does not require resorting to variational characterizations or blowing-up methods as in previous related proofs.