。
His story was so absurd that no one believed it.
Literal
His story [topic-は] too-much foolish was [reason-ので] no-one believed-not.
The pattern [adjective]+ので chains a cause to a result. ので is a less assertive 'because' than から — it presents the reason as objective rather than as the speaker's claim. あまりにも ('too much, excessively') intensifies the predicate. 馬鹿げる ('to seem foolish') is a ~げる verb form derived from 馬鹿. 誰も + negative is the 'no one' construction.