Summary
- Ahsoka Tano believed Anakin Skywalker was dead after Order 66 because she couldn't sense his presence in the Force anymore.
- Ahsoka had seen Anakin flirt with the dark side before, but couldn't fathom that he would betray everyone.
- Anakin truly became Darth Vader when he gave himself up to Palpatine, and Ahsoka had to physically see him as Vader to come to terms with what he had become.
Star Wars: The Clone Wars showrunner Dave Filoni explained why Ahsoka Tano believed Anakin Skywalker was dead after Order 66. As things unfold in the Siege of Mandalore arc, Ahsoka can feel Anakin's pain through the Force as he saves Palpatine and turns to the dark side. While she doesn't know what specifically transpired on Coruscant, Ahsoka can sense that something terrible happened to her friend.
In a 2016 interview with Star Wars, Filoni revealed that Ahsoka couldn't sense Anakin's presence in the Force after Order 66.
"This is something that George [Lucas] and I talked about. When Order 66 is called and Ahsoka survives it, she has a moment where she reaches out into the Force and she looks for Anakin’s presence. She could feel Anakin’s presence in the Force, no matter where she was in the galaxy. It’s not like a metal detector — she couldn’t just go right to where he was, but she would get a feeling that her friend is still safe and alive. When she reaches out after Order 66, she doesn’t get that. It’s gone, and so she believes him to be dead."
Things play out a bit differently in the final version of the Siege of Mandalore, but Anakin's lacking presence in the Force remains the same. There's an argument to be made that Anakin truly became Darth Vader at different points in Star Wars: Episode III – Revenge of the Sith, but giving himself up to Palpatine is the defining moment from Filoni's perspective.
Did Ahsoka Consider Anakin's Turn To The Dark Side? 
For someone as powerful as Anakin, one would think Ahsoka considered the possibility that he survived Order 66. Ahsoka had also seen Anakin flirt with the dark side as his student, and sensing the events in Palpatine's office would be familiar to those moments. While Ahsoka can't fathom the possibility that the good person she saw in Anakin would betray everyone, it had to be something for her to consider.
