"In the unlikely event"

Solution 1:

It's simply an idiom -- "an expression whose meaning is different from the meaning of the individual words" -- meaning "if this unlikely thing actually happens."

While some idioms have interesting origins, this one likely arose as a means of injecting a note of reassurance into a mention of a dire event.

Solution 2:

In looking at Google ngrams and the Google book quotes that are the underlyong sources, the phrase in the unlikely event goes back to at least as early as 1809 discussing the "recurrence of measures calculated to diminish the profits of tillage."

A quick scan of various uses through the 19th and ealry twentieth centurt seem to refer to mostly financial, commercial and political unlikely events. There is a signifcant uptick in the usage in the middle and later twentieth century, with what looks like much more usage relating to political risks.

These observations are based on written examples, and most people may now be familiar with its usage in spoken safety instructions. While it may have become a commonplace, its meaning is fairly straightforward, and it is shorter than saying

We really don't think this is going to happen, and we surely do not want you to worry, but just in case . . .