I solved an interesting problem in probability, and I think it's worth publishing as an interesting application. However, I am not a mathematician and don't know anything about existing journals or conferences where my problem may fit.
Is there a comprehensive guide with all the important journals and conferences in math, with an explanation of what kind of papers they may publish?
You mention that you are not a mathematician and that you feel that your solution to a math problem is worth publishing. If you are an undergraduate, you might want to consider journals targeted at authors who are undergraduates (search the internet for "undergraduate math journal").
If you are not an undergraduate (or even if you are), I recommend you look at the three journals published by the Mathematics Association of America:
- Mathematics Magazine "offers lively, readable, and appealing exposition on a wide range of mathematical topics." (Read more about it here.)
- The College Mathematics Journal "is designed to enhance classroom learning and stimulate thinking regarding undergraduate mathematics. It publishes articles, short Classroom Capsules, problems, solutions, media reviews and other pieces. All are aimed at the college mathematics curriculum with emphasis on topics taught in the first two years." (Read more about it here.)
- The American Mathematical Monthly "publishes articles, notes, and other features about mathematics and the profession. Its readers span a broad spectrum of mathematical interests and abilities. Authors are invited to submit articles and notes that bring interesting mathematical ideas to a wide audience of Monthly readers."