Well lets see from a source ....Imponderables: (Four Imponderables). Four things that Buddha warned against. One of these was trying to get into Karmic detail and look to find the "results" of volitional actions (Karma). It is enough to just Know and Understand and Intuitively have insight into the Fact that Volitional Action (karma) begets a result (Vipaka). It is even impossible to judge good and bad because that leads to the intellectual trap of duality and it's Dukkha. From the Pali Canon.... "These four imponderables are not to be speculated about. Whoever speculates about them would go mad & experience vexation. Which four?
The Buddha-range of the Buddhas (i.e., the range of powers a Buddha develops as a result of becoming a Buddha)...
The jhana-range of one absorbed in jhana (i.e., the range of powers that one may obtain while absorbed in jhana)....
The results of kamma...
Speculation about (the first moment, purpose, etc., of) the cosmos is an imponderable that is not to be speculated about. Whoever speculates about these things would go mad and experience vexation."
and the question being...."why they believe that Buddhas can foretell future events
Well the simple answer for me being simple
it is considered or infered perhaps in the first statement, that the one negates the other....the simple answer would be that as finately limited individuals we cannot fathom such things of possibility.....a buddha may.
I can watch someone do any number of things I may not do. By physical or other limitation I can go mad trying to do what they do saying I am human as they are so I may then do it....well we can see why that is so. So for us human we cannot do these things. Is that necessarily saying a buddha may not do these things.
I should then go mad and consider these things.....hmmm..perhaps not. But as to future events we can see by evidence of scriptual source that a buddha may predict certain futures.
And others may have some certain powers we may observe that indicates they may a bit see future events, so antedotally we may also know of that as possibility.
So we could on that basis reasonably assert a buddha may foretell the future yet ourselves personally find no reason to suspect we may as well. We have the same nature but we are not conventionally in this realm the same.
Faith....doesn't seem to be the final basis of this thing. Perhaps in a way, as faith we have in sutra sutta or jakata tale perhaps to be saying with some variance but not a whole lot of variance..... what the buddha intended...so yes that is faith of a sort.
But faith this is some miraculous power as the theist claim, other powered....seems not that faith.
To add to the comments already offered perhaps saying the same thing but from a simple perspective.
Or perhaaps the question is meaning something different and I am reading it wrong.
"This order considers that progress can be achieved more rapidly during a single month of self-transformation through terrifying conditions in rough terrain and in "the abode of harmful forces" than through meditating for a period of three years in towns and monasteries"....Takpo Tashi Namgyal.