As always, context matters. There are some cues:
"-줄 알다" as "can" or "have the ability to" is paired with future tense -ㄹ.
저는 영어를 할 줄 알아요. = I know how to speak English.
(X) 저는 영어를 하는 줄 알아요.
(X) 저는 영어를 한 줄 알아요.
On the other hand, present/past tense is possible for "think":
비가 올 줄 알았다. = I thought it would rain.
비가 오는 줄 알았다. = I thought it was raining.
비가 온 줄 알았다. = I thought it had rained.
If "-줄 알다" means "[I/you/he/she/...] think that...", then it is usually in past tense ("I thought ..."), or the subject is not "I". In other words, this form is not used to mean "I think that...".
비가 올 줄 알았다. = I thought it would rain.
(??) 비가 올 줄 안다. (Cannot mean "I think it would rain.")
(cf. 비가 올 것 같다. = I think it would rain.)
그럴 줄 알았다. = I knew this would happen.
Present tense is possible with other subjects, but I think in this case it usually means "think X even though it's not (likely) true":
내가 그런다고 그만둘 줄 아니? = Do you think I would stop at this?
저 고양이는 자기가 주인인 줄 안다. = That cat thinks it's the master.
Finally, note that 비가, 내가, 자기가 above are all using -이/가, instead of -은/는. This is because they are inside the subordinate clause:
저 고양이는 [자기가 주인인 줄] 안다. = That cat thinks [it's the master].
So, to conclude:
그 사람은 운전할 줄 알아요. = He knows how to drive.
(저는) 그 사람이 운전할 줄 알았어요. = I thought he would drive.
So, the sentence in question, I think "그 사람은 운전할 줄 알았어요" is ambiguous, because it's a bit "equally unusual" either way:
If it means "can", then one would normally use "알아요", because "being able to drive" is normally not something you would put in past tense: if you could drive yesterday, you are still able to drive today. Note that "-줄 알아요" always means capability: is not used for being authorized to do something (as in "You can go home after you finish this").
If it means "to think", then it should normally be "그 사람이". However, one could think of a situation to use "-은" (with accent) to signify contrast:
저는 걷는 게 편해서 걸어왔어요. 하지만 그 사람은 운전할 줄 알았어요. = I walked here because I like walking, but I thought he would drive.
Now, you might think this is all extremely complicated, but when you think about it, it's not much more complicated than deciding whether "He must be in the room." means "I'm sure he's in the room." or "I hereby order him to stay in the room." :)