That's an extremely difficult question to answer. For many ancient prophecies, we simply do not have enough evidence of either when the prophecy was actually recorded or whether the events actually came to pass.
To use the example given earlier of Jesus being born in Bethlehem, there are no contemporary sources (despite the obsession of the Romans with recording contemporary events and extensive Jewish writings from the same time period) that indicate Jesus even existed much less where he was born. Christians take it as an article of faith of course that this occurred and it is recorded as such in their bible. Many Christians also believe that their bible is a contemporary source, although scholars dispute when it was likely written due to textual clues.
To be fair, the same is true of Jewish sources. The Jewish bible records a prophecy that the Jewish people would be enslaved in Egypt and then freed, but the prophecy is vague at first glance and there is no real scientific evidence of the Exodus. However, the Jewish people take it as an article of faith that the Torah is correct that the Exodus occurred.
In a nutshell, it's all whether you want to believe in the prediction . . . and how you interpret the prediction in the first place.