"I thought that he was probably wrong" or "I thought he was probably wrong" which one is correct?
From additional comments currently below your question, you are right that I thought he seems more common than I thought that he.
This is from Google Books NGram Viewer. It shows the frequency of words in books that it tracks. (But note that it doesn't track verbal or conversational use of words.)
So, in terms of usage, you could say that the former is more idiomatic. (Again, if just considering printed material.) It also explains why your searches would turn up more instances of one versus the other.
But there are many words and constructions that are seldom used that are still grammatical—even if they aren't as common.
In terms of actual grammar in this case, both sentences are fine.
Many people think it sounds more natural to drop that as much as possible. In other words, they think it's a filler word that is used too often. That may or may not be true (it's a matter of style and opinion), but the use of that is still grammatical—even if its not always used.