However... high profile attornies do not usually agree to represent anyone unless they believe 100% in their client's innocence.
I disagree with this. Every attorney I have ever known, high profile or not, will take a case if the client can pay his or her fee. Of course, a high profile attorney can pick and choose the cases they want -- but if they take only those of defendants they believe are factually innocent, they will won't be taking many cases. Usually, it doesn't matter whether a client is in fact innocent or guilty -- that has no bearing on the case at all in terms of the zealous advocacy provided by the attorney. Once in awhile, they will take interesting cases in which they think the defendant deserves their expertise or which benefits the attorney in some way (very interesting case, more publicity, as a favor to someone). Sometimes they reduce or waive their fees. But I would never think an attorney would take a case merely because they believe someone is factually innocent. No matter what, there is no way to know for sure unless they have proof positive, and the attorney's beliefs don't matter.
I have met a whole lot of criminal defense attorneys and I have never met one who believed 100% in their client's innocence either before or after trial. Rarely, a client who has been convicted will have seemed to be factually innocent to the attorney all along, but the attorney doesn't know that for sure. Even more rarely, the convicted defendant will actually be factually innocent. In cases like these, the attorney, like everyone else, has opinions, but they are never 100% sure. The cases in which they think a convicted client was innocent haunt them -- mostly because there is no evidence available to absolutely prove that, so the facts found by the jury stand.
Two cases like this stand out in my mind, both defendants were convicted of first degree murder. In one, the attorney believes (but does not KNOW) that the defendant was convicted based on evidence that was the result of a shoddy investigation by LE. The appeals are over and there has never been absolute proof that the defendant was factually innocent. The attorney thinks the defendant is innocent (not 100%) and the defendant still says he is.
In the other, the attorney believed that the defendant was factually innocent *and* appealed the conviction based on insufficient evidence to prove, beyond a reasonable doubt, every element of the crime charged (first degree murder). In this case, after the appeals were over, the defendant told the attorney that he was in fact guilty, and the hitherto hidden back story was told in full detail to the attorney. It is still arguable, for the sake of discussion only, that there was insufficient evidence of guilt -- but the appellate courts did not agree.