It hadn't meant to be overheard. Ozai probably never wanted it to get out that he had three children instead of just Azula and Zuko. But it had. And it had peaked Azula's curiosity. After all, how did the youngest of the Firelords children just vanish? Azula left the palace, intending to track you down. She had briefly found Zuko and Iroh before. How hard could it be to find you?

After boarding a Fire Nation ship, Azula alternated between working on her bending and lighting generation and making sure things were running as efficiently as she wanted them to. Hours turn to days. Days to weeks. Weeks to months. Finally they hit land.

"Fancy seeing you here Zuzu."

Azula greeted Zuko. The two had never got along. Hell, she hated Zuko. She didn't like Iroh much either. But, if nothing else, the princess knew that they would be as intrigued as she about a long lost royal family member.

Zuko looked at Azula, his golden amber eyes meeting her own. He was wary, and rightfully so.

"What are you doing here?"

Azula replied back to her brother, her voice calm, as if she were discussing the weather.

"We have a long lost sibling. It seems fitting that we should search for him or her."

And like that, Azula knew she had Iroh and Zuko hooked. They would join her in the journey to find you if for no other reason then curiosity.