Read at your own risk if you haven't watched the first four episodes.
In episode 4, we found out Ha-Won's father is actually her 'adoptive' father. We have no idea how it happened. However, we were given a clue the adoptive father might be searching for Ha-Won's biological father with the surname Kang.
Is this a coincidence?
Probably not. Here are my thoughts: 1. The writer might be hinting Ha-won could be one of Grandpa Kang's descendant. Which gives the entitlement to be considered as candidate for the heir. 2. The writer is tricking us into think she's related but actually the man the father is looking for is Ji-woon's father.