I have a challenging excel problem

[Lyle Lazarus]

Hi guys, 

Have got quite a challenging problem. 

I'm trying to build a model that produces the probability of horses winning a race. 
There are 4 "speedmaps" (i.e. scenarios of how the race might play out) and each scenario has a percentage of how likely it is to happen. There are 3 horses in the race. 

So, 
Speedmap 1 (happens 40% of the time)
Horse A wins 70%
Horse B wins 25%
Horse C wins 5%

Speedmap 2 (happens 30% of the time)
Horse A wins 30%
Horse B wins 50%
Horse C wins 20%

Speedmap 3 (happens 20% of the time)
Horse A wins 10%
Horse B wins 20%
Horse C wins 70%

Speedmap 4 (happens 10% of the time)
Horse A wins 80%
Horse B wins 10%
Horse C wins 10%

I manually worked out that for this race, the probability of each horse winning is: A = 47%, B=30%, C=23%

How do I build a model in excel where I can input any values in and the probability of the horses winning is spat out? 

Would appreciate any help/discussion!!
Thanks!

[#2]

@Lyle Lazarus 

I think you need to give more information. What values are you entering? You can generate a random number between 1 and 10 and assign values of - 10,20,20,30,30,30,40,40,40,40 -. That would tell you which "Speed map" to use. So, I'm guessing, you get 3 friends to each select a horse. Then run the random number generator. Then that will show which horse won?

[#3]

@Lyle Lazarus 

To get the figures you show either calculate the probability for each horse individually

= SUMPRODUCT( HorseA, Likelihood )

= SUMPRODUCT( HorseB, Likelihood )

= SUMPRODUCT( HorseC, Likelihood )

or as a single calculation

= MMULT( speedmaps, TRANSPOSE(Likelihood) )

[committed with CSE]

where 'Likelihood' is the probability for each speedmap.