One of the more interesting facts about the biogeography of Hawaii is that mosquitoes were not always present; they only arrived in the early nineteenth century, as stowaways aboard oceangoing ships. The explanation for this is straightforward; Hawaii is not a splinter of a continent; it is a volcanic island that emerged pristine from the ocean, and is thousands of kilometers from the nearest continent; distance protected it, until that protective barrier was breached.
As far as I know, Hawaii is the only such case, i.e. the only nontrivial tropical ecosystem that is known to have been mosquito-free until recently.
Just how much distance is needed to serve as a barrier? I gather mosquitoes can only fly a couple of kilometers normally, but presumably the tail end of the distribution will be much longer thanks to the occasional one being swept up in a freak storm etc.
Or, for concrete numbers: suppose you have two continents, both with wet tropical climates, suitable habitat for mosquitoes, one of which has them, the other not. How wide a stretch of unbroken ocean would suffice for a less than fifty percent probability of mosquitoes reaching and becoming established on the second continent in a million years, assuming no surprising geological events like ice ages, and no intelligent agency?