I wouldn't say there's 'almost none' in Europe, but the global distribution of petroleum is uneven. The reason is that petroleum systems need a convergence of conditions that is relatively rare.

For a start, the comment about the inappropriateness of a political map for this purpose is spot on. [This USGS map][1] of global petroleum systems, and non-petroleum-rich basins, is much better — apart from the fact that it perversely omits the USA's substantial endowment: 

![World petroleum systems][2]

These 'petroleum systems' are essentially modern or ancient sedimentary basins with a particular combination of features. I'll refer to a previous answer about a specific region: [Why would there be no hydrocarbons in the Sveconorwegian belt?](https://earthscience.stackexchange.com/questions/2811/why-would-there-be-no-hydrocarbons-in-the-sveconorwegian-belt/2819#2819) Paraphrasing, and self-plagiarizing, here's what you need for a hydrocarbon (oil or gas) accumulation:

> - A [kerogen][3]-rich source rock that has been 'cooked' to thermal maturity. So you need lots of organic matter, burial, and time.
> - A migration pathway from the source to a trapping configuration, and time for this to have happened.
> - A structural or stratigraphic trap, such as an anticline, and the geological conditions that have preserved it since filling.
> - A reservoir rock — a porous and permeable rock. Usually this is a sedimentary rock (like sandstone, which there's lots of in Saudi!).
> 
> Only 'conventional' hydrocarbon deposits, such as you might find in
> the North Sea, Saudi Arabia, or the Gulf of Mexico, need all these
> conditions. 'Shale gas' is basically just a mature source rock — we
> can extract hydrocarbons from it by fracking, for example.

So the map of global petroleum resources is a map of places where these criteria converge. Certain deltas are prolific (Mississippi, Niger), because you have rapid burial of sand and organic material. In other places, one or more of the conditions has not been met. Much of Canada, for example, is exposed basement granite: none of the components are there.

The unevenness is exacerbated by [the Pareto distribution][4] of system productivity — as with most natural things, we have a few giants, and a long tail. So [the WCSB][5] and Saudi stick out as anomalous, making the distribution even more 'lumpy'.


  [1]: https://upload.wikimedia.org/wikipedia/commons/thumb/b/b3/World_petroleum_systems.png/1280px-World_petroleum_systems.png
  [2]: https://i.sstatic.net/epJ9z.png
  [3]: https://en.wikipedia.org/wiki/Kerogen
  [4]: https://en.wikipedia.org/wiki/Pareto_distribution
  [5]: https://en.wikipedia.org/wiki/Western_Canadian_Sedimentary_Basin