i have also heard that davening (obviously) makes you have a closer connection with HAsehm. and now that you have a closer connection to HAshem, you are a different person. therefore, what was best for you b4 you davened istnt what is now best for now that you have davened. instead, their is a diffrent thing that is best for you.
in other words, the act of teffila changes what is best for you, and therefore, by definition, what HAshem does for you.
(e.g. if tzaros were supposed to happen to you to make you closer to HAshem, or to give you a kapara, but then since you accomplished that same thing by teffila, the zaros are unnecessary)
however, this does not explain davening for others, whom are not brought closer to HAshem by your teffilos (as far as i now know)