There's only one true invisibility cloak, and it's not enough to get someone out on its own.
Everything else needed to escape is readily available, given that people sneaking in with patronuses is a regular occurance. The owner of the cloak could easily have been sneaking someone out every few months.
What reason to we have to suppose that the aurors or the designers of Azkaban ever bothered to consider the question of whether it would hide someone from dementors?
The fact that no one in the story is supposed to be holding an idiot ball. The fact that no one is supposed to be able to escape the dementors notice is the central element of Askaban's security, so much so that they barely put up a token effort of guarding against break-ins. If they considered this merely a hiding problem then to never ever have considered whether it might be possible to hide from them after all, or to not have considered a legendary item of hiding in that context would be pretty incompetent.
The aurors were surprised that Bellatrix had vanished from the senses of the dementors, but this is clearly an unusual occurrence that should not arise within ordinary experience, so we should not be surprised at their surprise. They do not have "someone sneaked in with the true invisibility cloak" as a cached explanation to check for plausibility in this situation.
There were dozens of them and they had about two hours to think about it. If they considered it merely a hiding problem at least one of them should have raised the possibility. When confronted with something apparently impossible powerful magic is a rather obvious answer.
Given that we don't even know the approximate ages of either, Azkaban may even predate the true invisibility cloak's creation.
Seems unlikely since ancient powerful magic keeps getting lost, the cloak looks like ancient powerful magic, but Askaban doesn't seem to incorporate anything unreproducible. Even if Askaban predated the cloak that would still mean no one between the time the cloak became public knowledge and the current day made the necessary adjustments to Askaban security.
If they considered this merely a hiding problem then to never ever have considered whether it might be possible to hide from them after all, or to not have considered a legendary item of hiding in that context would be pretty incompetent.
My impression was that it was legendary in the sense of "yeah, we tell those stories to our children" instead of "look, every student's sat under the Sorting Hat, it exists and there are thousands of witnesses." That's an unfortunate part of magical stories- it's hard to avoid the Every Rumor Is Comp...
- This thread has run its course. You will find newer threads in the discussion section.
Another discussion thread - the fourth - has reached the (arbitrary?) 500 comments threshold, so it's time for a new thread for Eliezer Yudkowsky's widely-praised Harry Potter fanfic.
Most of the paratext and fan-made resources are listed on Mr. LessWrong's author page. There is also AdeleneDawner's collection of most of the previously-published Author's Notes.
Older threads: one, two, three, four. By tag.
Newer threads are in the Discussion section, starting from Part 6.
Spoiler policy as suggested by Unnamed and approved by Eliezer, me, and at least three other upmodders:
It would also be quite sensible and welcome to continue the practice of declaring at the top of your post which chapters you are about to discuss, especially for newly-published ones, so that people who haven't yet seen them can stop reading in time.