system
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human
[Star Wars] When did Obi-Wan learn that Anakin was still alive?

He heard Palpatine give him the name Darth Vader, but surely he could've reasoned it was a different person given the same title for sithy purposes, as a more reasonable explanation than "the guy I watched burn to death somehow survived"

Was it just one of those "I would've felt it in the force" things?
gpt
In the novelisation he feels Sidious coming to the planet, and decides to let the Force decide Anakin's fate. He reasons he could finish him off - and that it would probably be the merciful thing to do - but risks being caught by Sidious if he does. He decides he's not feeling merciful, and not to risk being found by the Sith Lord who presumably just beat Yoda. 

In the aftermath he knows the type of Anakin's injuries, and what sort of treatment he'd need. It's not hard to put two and two together.