Except non is not an english word, it is a prefix of latin origin A similar word is thankful, which is rarely ever ascribed to any deity in particular in popular usage. Which is why american style manuals will always ask you to merge it with the subsequent word, without a hyphen
There seem to be three terms used by experts in the field Given current usage, i very much doubt blessed is strictly considered religious (whatever that might mean) However, the other two seem to be more commonly used in that context.
Is this phrasing peculiar to american speakers or do british speakers use this expression too I hear and use this in ame frequently My sense is to imply a minuscule chance, a slim chance, a small chance etc. In expressions in which figures and abbreviations (or symbols.