As for Duke Albert, he was greatly interested in the Adventurers—which Pedro himself wanted to look after to the point that he even went away from what he was supposed to do as a BHO Officer. And there was no better way to observe them but by being present in the Adventurer's Guild by himself.
Besides, it was beneficial for him to do so because adventurers would eventually enter the Kingdom for different reasons, sooner or later. So, it was critical to gain as much information as he can from this opportunity.
On top of that, Duke Albert has the highest probability of being the next King of the Tarala Kingdom. So, he would eventually need to know a thing or two about the adventurers to prepare for the adjustments he needs to make to accommodate them into the Kingdom.