I was reading an article about Baylan's disappointment in Anakin. As if he wanted Anakin to be the chosen one until order 66.
It just occurred to me... Could Baylan be Anakin's father? Or, at least be responsible for Anakin's existence? Maybe he used the force to impregnate Anakin's mom without her knowledge so he could bring forth the "chosen one." He'd have to hold onto that secret for the rest of his life, or Baylan could be held accountable for attempting to manipulate the prophecy, leading to the deaths of billions. Baylan might feel personally responsible for the fall of the Republic and the Jedi. Now, he's obsessed with fixing his mistake.
This might be why Baylan knows that Anakin became Vader. Baylan is connected to him personally through the force and maybe also by blood. Baylan probably didn't even need to be near Anakin to know when he turned to the dark side. He could feel it from across the galaxy.