Statistical modelling of finishing position from a finite number of participants

[Ominous]

I want to extraploate some data of finishing positions in eurovision song contest and I ran into some problems.

The basic idea is that betfair offers chance for top10 and chance for top 4 out of the 25 particiapnts and I want to assume that these chancs are correct and model chances for topx where x is an arbitary number.

I first thought of using a normal distribution modelled to fit with the betfair data but I doubt this is wise. This modell will give all medicore participants most chance to end up in the range of place 10-15 which can obviously not be true as they compete with each others and each spot can only be filled once.

Is thier an alternative statistical function that can be used? Is there another way around this problem?

Greatful for respons

[TomG]

Google search "Harville Formula." Its original application is horse racing but it can be used to solve your problem.

[Ominous]

Thank you for your input. I read about the "Harville Formula" but tbh I doubt it will produce a good estimate for my purposes. (I mean, the accuracy of the estimate is bound to decrease the more places after the first that is calculated with the harville formula and while it may be useful for calc chance for second place I highly doubt that its useful for calculating the chance of the 9th place for instance)

I found some other resources though,

http://www.financialmathematics.com/wiki/Code:gevrace

Above is Matlab code which claims to be able to calculate what I am intrested in, problem is that I dont quite understand it yet even though Ive taken one advanced course in statistics.
Maybe someone can help me out here, do you think the above program is good for my purposes and will Generalized_extreme_value_distribution work for this application?

http://en.wikipedia.org/wiki/Generalized_extreme_value_distribution