It's all AU.

The Professor was sitting in the lobby of the hotel with a book and a cup of tea. He was reading Shakespeare, since Estelle had told him she'd met the man himself, and he'd decided he should read something a little closer to the source than the version that had been through a hundred trillion years of translations.

He reached over for his tea and saw a woman enter the hotel, looking around as if she'd lost something.

"Are you looking for someone?" he asked, kindly.

The Master had wandered down to the lake again, searching for a bit of peace and quiet. A nice stretch of still water often had a calming effect on the drums. He'd had a lovely holiday with Lucy once in the Lake District – the drums had been the quietest he'd known them since before the destruction of Gallifrey.

He stood at the edge of the lake near where he had met Professor Yana and gazed out across the water, letting the peace soak into him.