Exactly. P(results|luck) and P(luck|results) are two very different things. We don't know the probability that the results are due to "just luck" (whatever that means).
I think it's quite dramatic how many very intelligent people (up to writers in major publications) are uneducated about this distinction, and how dramatically wrong decisions can be if this is misunderstood. If we could teach this, as well as correlation vs causation, I'm convinced the intelligent public would make much better decisions about many things, medicine and nutrition to name a couple.