From Longman Dictionary of Contemporary Englishthe balance of evidence/probability etcthe balance of evidence/probability etcPROBABLYthe most likely answer or result produced by opposing information, reasons etc → balance
Examples from the Corpus
the balance of evidence/probability etc• The burden of proof in establishing the defence is upon the defendant on the balance of probabilities.• All those defences are for the defendant to establish on the balance of probabilities.• A decision is made only on the balance of probabilities.• After looking at the credentials for miraculous claims, Hume came to the conclusion that the balance of probabilities counted against them. 