position to insert element in inserionsort (equality of probablity)
Try counting the number of permutations where it is inserted in position $i$.  How does this number depend on $i$?  That will lead immediately to a proof.

In general, when you need to calculate a probability of some event, and you have a uniform distribution, one way is to use counting to compute the probability: count the number of outcomes where the event is true, and then divide by the total number of possible outcomes.