Cambridge Grammar of English Hardback with cd-rom a comprehensive Guide

On condition that, in the event that, in the event of + noun phrase

On condition that

and in the event that/in the event of are much more frequent in

formal written contexts than in informal spoken contexts. They may be used for

real and unreal conditions:

[from a leaflet published by an anti-smoking campaign]

Many surgeons offer patients an operation only 

on condition that they give up

smoking – and often find that the ensuing improvement makes surgery

unnecessary. 

In the event that the plane lands on water, life-jackets are located under every

seat.

In the event of a sudden loss of cabin pressure, oxygen masks will be lowered

automatically from the panel above your seat.