How likely would a black person be chosen as the Prime Minister of the UK, assuming the UK Prime Minister would be the equivalent of the US President?

The PM is not the equivalent of the President. The PM is simply the leader of whatever political party happens to hold the most seats in Parliament, so the question is actually, how likely is it that a major political party would choose a black leader?

There is absolutely nothing against it on race grounds. If anything, being black might slightly improve a person’s chances of being picked for leader, as the party might feel that being shown to be inclusive would improve their share of the young person’s votes.

However, the black community is both small and disproportionately made up of people whose families only moved to the UK in the mid 20th C. The top ranks of the political parties are still afaik disproportionately made up of people who went to public school. [In British terms, a public school is a very old and grand fee-paying school, called “public” because some of them are so old that “public” meant “not just training students for the priesthood”.]

At present, there are not that many black families who can afford to send their children to very expensive fee-paying schools, so that reduces their presence in the top ranks of politics (except Diane Abbott). But over time we have more and more successful black bankers and business(wo)men able to afford expensive school fees, and politicians become more egalitarian, and either way the likelihood of a black head of party becomes more likely.

However, we’ll probably have a South Asian PM first, because the South Asian community is much bigger.