It makes sense for the prince to suspect that since he didn't know about the truth. Considering all the politics around his engagement to the fake Han Sangyul, it would make sense for him to assume there are other parties with different interests. It's especially suspicious when the real is disguised and a fake is put in place. For someone who knows nothing it makes sense to assume the real Han Sangyul has a different motive too.
It makes sense for the prince to suspect that since he didn't know about the truth. Considering all the politics around his engagement to the fake Han Sangyul, it would make sense for him to assume there are other parties with different interests. It's especially suspicious when the real is disguised and a fake is put in place. For someone who knows nothing it makes sense to assume the real Han Sangyul has a different motive too.