Yes I suppose, but he still needed to learn that Vader was still around. And if the news of some Sith Lord in a black suite called Darth Vader roaming the galaxy reached Obi-Wan, I am sure that he caught some whispers and stories of Inquisitors and this Vader hunting rouge Jedi too.
JEDIT: Didn’t knew Vader made the news. But either way Obi had 19 years to hear stories about Jedi being hunted down and connect the dots.