Quark talks about the election of a new Kai. This makes sense because Winn is dead. But how does anyone know that? The only witnesses to her death were Sisko and Dukat. Sisko speaks to Kasidy later, but he only tell her what happened to him. He does not mention Winn. However, considering how long it would take for Kira to bring Odo to the Founders' Homeworld and return to Deep Space Nine (a few days' travel time at least), it is possible the Bajorans had come to the conclusion that Winn was dead, or at the very least were electing an interim Kai.