The general issue - Why questions that aren't really clear should be on hold:
Questions that are not clear are supposed to be put on hold so that they can be made clear before people start posting answers that misunderstand the question, causing problems for the asker as well as later readers (who are the actual target of a good answer under the Stack Exchange model).
Your feelings about how clear the question may be are not particularly relevant (except in so far as that makes it hard for you to see what to do). The central issue is how clear the average semi-knowledgeable reader is likely to find it. In the first place potential answerers need to clearly understand the question, but that alone isn't enough: by semi-knowledgeable readers I mean people who could read and benefit from an answer -- which is a much lower degree of understanding of statistics than required to make a good answer. If I (as a regular answerer with a reasonable level of understanding) find your question unclear -- and I don't seem to be alone, so it isn't just some odd quirk on my part -- the question would fall short of being clear enough.
Specifics of what is unclear:
I explained issues with the post in an extended comment under the post, but I think the main issues were:
the conflation of density with probability made it difficult to see what objects you were actually manipulating; it almost seems as if you were flipping between a set of probabilities and a density (specifying probabilities at values and then somehow making a density from that?)
the process by which you obtained and possibly manipulated these quantities was not sufficiently clear, making it hard to see how a model for that process might be constructed. Your comments here to gung indicate to me that this and the previous issue are still not clear enough. If you're taking information and then smoothing it before combining, why is that the best approach -- why not combine the original information instead ... and then smooth the result? If we don't know enough to answer that, we don't have a clear question. Is the quantity you're specifying probability for really discrete? If it is, don't make it into a density. If it's not discrete, what do the probabilities represent (what are they probabilities of?)
the part about convolution I initially found confusing because I couldn't see how it had anything to do with the problem -- if the previous issues had been clearer I think I'd have understood this earlier: I believe that's simply a misunderstanding that is best addressed in an answer. In effect it looks like you decided to try to solve a problem a particular way and asked about the problems you encountered with your attempted solution instead of asking how to solve your original problem. If I understand the situation correctly your solution is mistaken but we can address that as long as we have correctly understood what you have and what you want to get.
As a result I think the question would be much clearer if you removed almost all your information about your solution (apart from saying that using convolution was how you were thinking of solving it). I previously explained that I think all or almost almost all your code should be removed. Many of your plots (those about manipulating the convolution) add nothing to understanding your problem and I think they should be removed as well.
The question is definitely better than it was but some of my issues are not fully resolved.
In spite of these remaining misgivings I reopened on amoeba's request. If amoeba thinks it's answerable now I don't want to get in the way of that answer. I'd like it to made be clearer but an answer may indeed help clarify the question. However if an answer leaves the question as unclear as I still find it, I'll likely close it again -- I think there's a danger that not only might you end up with an answer that doesn't address the actual problem you have but one that may in turn confuse later readers with similar-sounding problems. Closure would at least flag that it needs to be treated with caution.
[I suspect the nub of an answer may be as simple as "Convolution is the wrong thing to do, you need to average the densities" (or probability functions or whatever these objects are), but even if that's right, details of the best way to do that would depend on information that I'm not sure is there yet.]