Why do you think fossil fuels are not distributed evenly across the globe?

Oil and natural gas are only found in certain places on earth because a number of rare events all must happen in the same place. Firstly, oil and gas will only be found in sedimentary basins so that limits possible worldwide territory considerably. Furthermore, all of the following have to take place:

1-Organic matter has to collect in hostile dead zone and the bottom of an ocean, lake or sea

2-This organic matter needs to be buried at a shallow depth, becoming a kerogen source rock

3-This source rock needs to be buried more deeply until pressure/temperature conditions are in the oil/gas generating window

4-The source rock needs to be at this depth for significant time to "cook" and release oil or gas

5-The oil/gas must migrate to a reservoir quality rock with enough porosity and permeability to allow oil to be stored within it and flow through at an economically viable rate.

6-The oil/gas must be trapped in the reservoir: sufficiently impermeable shale or salt layers must be oriented so that the oil/gas which is more buoyant than water does not escape. (Slightly more complicated when the reservoir is directly adjacent to the source rock)

People have to find the oil and it has to be economical to bring it to market (this makes more remote areas like the Arctic less likely to have oil/gas production)