Perfect secrecy and known ciphertext length From what I understand perfect secrecy means that the probability distribution of the messages are independent of the cipertext, right? How can the one time-pad be perfectly secret when the ciphertext is as long as the message in terms of bits?

Because for a given ciphertext I could for example know that my message is not longer than my ciphertext and therefore I could say that a given message occurs with higher probability?
You are correct that the security provided by a one-time pad is that a chosen-plaintext attacker can't distinguish between two messages of the same length, at least not with better advantage than their advantage at distinguishing the pad itself from uniform random.

Length, of course, can be a side channel for more interesting information, especially if variable-rate compression is involved!  For example, the distribution of page sizes when downloading Wikipedia is likely to be very different from the distribution of file sizes when downloading the WikiLeaks archive.

If you have a maximum message length, you could extend your messages up to that maximum length with (say) zeros.  But this can be costlier.  Alternatively, you could break messages up into chunks.  In any case, message length is something that a protocol designer must consider when striving for confidentiality!