I have a series of problems that involve events that happen one after another, and where the usual formulas like $P(\frac{A}{B})=\frac{P(AB)}{P(A)}$ don't seem to help.
Example:
In a horse race there are $3$ horses. $E12$ means horse $1$ finishes before horse $2$. $E123$ means horse $1$ finishes before $2$, which finishes before $3,$ etc.
If $P(E13)=2/3$ and $P(E23)=1/2$ then $P(E123)=?$
How can I go about solving this kind of problems?