I meant "... A feeds C ..." instead of B. The intent of the feeding and providing is to get B dead. C didn't ask for it.

This is cut and dried.

Intent --> Action --> if the result is murder, then Person A colluded in the murder.

The discussion is muddied by the other actors, which is why I removed them. Person A wanted Person B dead, and took actions to secure that result. Person A may have thought s/he was being subtle and obfuscatory about it, but it's conspiracy to commit murder.

It may be hard to prove, but it's highly likely in any real-world, non-hypothetical situation that there would be a trail of actions and comments that could be traced back to Person A once the initial clue (that Person A told Person C about the affair and how that conversation -- as well as any subsequent ones -- went) was discovered, including motive for colluding in a murder.

If you don't agree, compare and contrast the above to this:

How are these qualitatively different, aside from the relative certitude that a murder will actually occur? Depending on who Person C is, the outcome might be as certain as paying a murderer-for-hire to do the job.

Person A certainly thinks so; otherwise, it's a waste of time for achieving the premise of the Situation: a) Person A wants person B to die.

The difference is simple and self evident:

a) Person A wants person B to die
b) Person A sacrifices a chicken to satan and asks them to kill person B, believing Satan will kill person B

vs.

a) Person A wants person b to die
b) Person B mentions to person C that person A is made of chocolate pudding, knowing person C likes chocolate puding and believing person C will then kill and devour person A

so which of these is the more 'guilty' scenario? the first, because person A doesn't just *want* person a to die, they *ask* for person A to die. And in any situation where another intelligent being (or presumed intelligent being) is involved, that is a key component.
You are conflating the essence of the argument by assuming that person C kills person B, which is not relevant to person A's guilt. If i hire ahitman to kill the much disliked person B, and that hit man turns arround, takes my money and leaves town, I am just as guilty of attempting to hire someone to kill person B as if they had taken the money and finished the job.

It's all about whether or not the intention can be discovered. It's difficult to prove intent. Often times there's insufficient evidence, as opposed to evidence of action. In which case, person C will be punished (one would hope; because that's the law). And yes, first degree murder is illegal, but it can be difficult to prove in these scenarios.

It'd be up to a witness testimony from person C and whether or not the court is willing to listen to the person that commited the crime.

As I understand the original question, it was not concerned with the practicalities of potential prosecution, but with the appropriateness (if any) of pursuing prosecution even in the presence of hypothetical perfect knowledge of the events.

C could just tell the court that A told him about the affair, not what was A's intention, since C does not necessarily know of that intention.
But I also don't think that that was the principal point of this discussion. Proving this kind of intent would be very difficult.

In the same way that C cannot know what a's intent was, A cannot know what C's reaction will be. Unless a advocates a specific action for C their intent is irrelevant. If the road to hell can be paved with good intentions then the road to paradise can be paved with ill intentions.

Does murder get any more ethically correct if you manage to get away with it because some chain can't be discovered?

"The road to hell is paved with good intentions" means that people can do the worst things for the best of reasons.
"The road to paradise is paced with ill intentions" would only be applicable in this case if you believe that the intent to get someone killed is a bad one, but actually getting them killed is somehow good.

or if the outcome was something other than what was intended. Perhaps you tell C about b's affair hoping to get B killed but instead B and C have along discussion and wind up strengthening their relationship and resolving their differences. The OPs outcome is not a foregone conclusion just because a tells C about the affair, which is kind of my whole point. if hindsight proves A's assumptions correct that still does not mean A was guarunteed to be right.

The end result of firing a rifle at someone's head isn't a foregone conclusion, either. Your target could move unexpectedly at just the wrong moment. Your ammunition could fail. Your weapon could malfunction. You could just be an unskilled shooter, or a decent shooter attempting a shot beyond your skill. You could have delusions as to the degree of skill you have with such a weapon.
Many of these factors are, practically, unknowable by the individual making the attempt. None of them, individually or combined, are sufficient to make shooting a rifle at someone's head no longer illegal in most circumstances.