V tomhle použití se believe jako věřit dost dobře přeložit nedá.
2 : to hold as an opinion : suppose
I believe it will rain soon
You do the same thing in German - you often say "ich glaube" instead of "ich denke". Spanish prefers "creo" quite strongly. We don't do it in Czech, "věřit" is not really used to mean "to have an opinion", but to literally "believe".
For example: "Věřím, že to dobře dopadne." - I believe it will end well - it's more about faith and hope than about the purely mental/rational "myslet" (think).
That's why the Czech "myslet" can easily be expressed by both "think" and "believe" in many contexts, just like the English "believe" can mean "myslet" or "věřit", depending on its actual meaning.