We observe B, and have good evidence that 99.999% of the time B was causally preceded by A. We are, I think, pretty likely to say we know that A occurred. On the other hand, if we have good evidence that 99.999% of the time B is causally followed by C, a lot more people will be very cautious in affirming they know that C will occur.
The difference here does not, I think, depend on the mere fact that A is in the past and C is in the future. For, surely, if one is unwilling to say "I know I will fail to win the lottery" before the winner is picked, one will also be unwilling to say "I know I failed to win the lottery" after the winner has been picked but before one has heard who it is. It would be really weird to imagine someone sitting around in a closed room, watch in hand, and then as soon as noon comes, she says: "Now I know I failed to win the lottery", just because the winner is picked at noon.
It could be that this is just another example of widespread irrationality (when I wrote this post, which I am much less sure of now, I think this is what I would have said), but let us not have recourse to that immediately.
I am inclined to think the difference is not based on whether the knowledge claim is in the past or future, nor even on whether the knowledge claim is in the past or future of the evidence, but on the causal connection between the evidence and the event about which the knowledge claim is or is not made. We are, I think, much more willing to move epistemically from effects to causes than from causes to effects. If this willingness is not mistaken, then it follows that there can be probabilistically isomorphic epistemic situations in one of which one knows and in the other of which one does not.
Here is one line of thought on this. Perhaps we are confusing de re with de dicto knowledge. Suppose that Koons is right to say in Realism Regained that if D causes E, then it is possible to have D without E but not possible to have E without D. Then by knowing D de re, we cannot know E de re because many numerically different effects could follow the very same D. But by knowing E de re, we are in a position to know D de re, because no other cause could have produced this very E that we know de re.
And maybe this isn't just a confusion. For it may be that saying that I know that E occurs, or maybe implicates, that I de re know (am acquainted with?) E.
This is related to the scholastic idea that genuine knowledge is knowledge of the forms, and this is always by acquaintance.
A different line of thought on the asymmetry would be that one of our doxastic proper functions is gaining non-probabilistic beliefs about causes from effects, but we simply do not have a doxastic proper function of gaining non-probabilistic beliefs about effects from causes. A theist might even give an explanation of this: God hasn't designed us to gain non-probabilistic beliefs about effects from causes, as that would make miracles be deceptive.