I think= certainty or doubt?

In your example the doctor expresses an opinion, and in effect s/he is saying, of all the possible outcomes I believe this is the most likely, so no, it isn't certainty.


One example I can think of is a teacher saying to a misbehaving student "I think you should leave the room now." That is a command that means "Leave the room now"

Also, if the doctor followed this by winking and saying, "...of natural causes," this might express certainty through sarcasm and poor social skills.

I think it's up to the situations

sometimes means certainty,
sotimes means doubt,
in your example, I think it may mean "I'm sorry"

Sometimes it means "I am certain, but I'm too polite to point out how sure I am that you are wrong"

"I think, perhaps, you are not telling the truth young man!"