The encounter rates of Very Rare Pokemon widely vary between different VRs in different areas - this can apply to Pokemon of all rarities. Since the sum of all Pokemon encounters percentages in any area must equate to 100%, the encounter rate of a Pokemon could be more or less depending on other Pokemon spawns that surround it in the area; if there are more very rares in an area, for example (barring consideration of any other rarities), it would likely divvy up the odds, and they would have to be at a smaller percentage each to shape 100%. Contrariwise, if there are less Very Rare Pokemon in an area, one or more could have a more concentrated encounter rate.
Since the area is often congested with Pokemon of other rarity - common/rare/Very Rare/Horribly Rare - the encounter rate of a Very Rare typically lies within a specified range for Very Rare Pokemon. Based on the percentages that were disclosed for Very Rare and Horribly Rare Pokemon (0.005% and 0.0001%, respectively), the odds of very rare pokemon would equivalently range from 1/200 to 1/10,000.
The precise odds of the Pokemon encounters have not been documented anywhere, as they are fairly dynamic and could be altered depending on spawn changes made to the area, but if there are more Pokemon within an area, it's safe to assume that one of the rarer Pokemon may have a lower encounter rate, due to more common Pokemon popping up and interfering with its encounter rate.
Regarding shinies, the odds are constant at 1/8192 (or 1/2048 with membership benefits) for the shiny counterpart of any Pokemon; just bear in mind that the roll for the shiny outcome is independent from the encounter rate of the Pokemon itself.
