They were not convicted of anything, if you're referring to the Mexico/Iran story which I guess you are. You heard the US Government's side of the story. The USG agreed not to take the charges to court as long as HSBC accepted big fines and didn't say anything (i.e. didn't attempt to defend itself in public). So there was never any court case or any judicial process involved.
If you hear only the government's story and the other side is gagged, the listener will always conclude the perp is guilty. You can dig in and find the other side if you like: I did. The case looks a lot less clear, then. For instance HSBC was accused of laundering lots of money for Mexican drug cartels. Most people think that means "knowingly laundering". It doesn't: the money in question actually came from remittances firms. The American's case was something like this: there's so much money being remitted across the border, there must be drug money in there. HSBC is moving money for remittances firms. Therefore HSBC must be moving drug money without knowing. Therefore their AML standards are too low, therefore they are money laundering.
As you can see, I am not sympathetic to this kind of logic or "justice". Certainly the US case would not have been successful in court under the original definition as they never presented evidence any kind of conspiracy inside HSBC to launder drug money. The allegations revolved entirely around HSBC not trying hard enough, which is not the same thing.
Actual convictions for anti-money laundering offences are very rare. This kind of fine-and-silence outcome is much more common.
The reasons are simple. The current situation is kind of like a Cuban missile crisis. It's very volatile and unstable. Every banker knows that every banker is guilty of some kind of AML offence, because it's impossible to work in finance and not be guilty. The laws are just that badly written. What's more, western governments know this too. Almost every big bank has been fined under AML laws in the past 20 years or so.
But American justice is extremely vicious (and it's in America where the whole idea of anti-money-laundering originated). Like many laws, AML offences can carry 20 year jail sentences.
If you mix 20 year sentences with "everyone is guilty" you have a situation that is like a minefield. If the government actually started prosecuting bankers under these laws, there's a risk they might win and that could be apocalyptic - it could trigger a collapse of the entire financial system as bankers exited the industry en-masse.
In the HSBC case, one part of the US Gov (either Treasury or DoJ, I forget which) actually did want to prosecute. The other part convinced them not to, using the above logic. The chance of successfully jailing a banker is high enough that they can't actually do so, lest it cause the industry to self destruct.