British Citizen convicted in Australia with questions.

Hi, first time posting. Wonder if someone can answer my queries.

If someone has a conviction in Australia for example, but they are a British citizen but no longer reside in Australia, what’s the likelihood of them being refused entry into a country that enforces a ‘no criminal convictions’ policy? Will the prospective country of destination be aware of the conviction in Australia because it is somehow linked to their British passport, or will the destination country only receive information about a traveller’s country of citizenship? (Which in this case would be all clear).

Any info would be greatly appreciated.

Thanks.