Русско-англо-русский юридический словарь

Taking out a loan to buy a car or a house is common. Businesses use loans for start-ups, expansion and a variety of other reasons. When individuals or businesses need a loan, they talk to a loan officer at a financial institution, such as a bank, credit union or lending company. Loan officers help people apply for loans by gathering the information that determines the probability that the loan will be paid back. To be a loan officer requires good financial judgment coming from education and training. (wikiHow)

Further sanctions “would increase the probability of default given PDVSA’s already dire liquidity situation and because it would give Maduro a potential scapegoat to blame for the government’s inability to pay,” said Risa Grais-Targow, a senior analyst at Eurasia Group in Washington. (Bloomberg)

The civil standard of proof is proof on a balance of probabilities. The criminal standard is proof beyond a reasonable doubt. This article deals with civil standards of proof. Saying something is proven on a balance of probabilities means that it is more likely than not to have occurred. It means that it is probable, i.e., the probability that some event happens is more than 50%. So mathematically proof on a balance of probabilities is 50.1% likelihood of something having occurred. (website of Bayda Disability Law Firm)

Ah, if you mean that there's a difference in meaning between "the decision to close" and "the decision on closing/the decision about closing", then I agree - "the decision on/about closing" could even mean "the decision against closing":). [...]

In Her decision to leave school shocked her family, we know that she decided to leave school.

In Her decision about leaving school shocked her family, we know that she made a decision about leaving school, but we don't know what that decision was - maybe she decided not to leave, maybe she decided to postpone thinking about leaving for a while. The probability is that she made a decision to leave; but we don't know that for sure.

Grammatically, both Her decision to leave school shocked her family and Her decision about leaving school shocked her family are both fine - but they don't have identical meanings. (WordReference.com)