I have $n$ cards, however, I like only 1 card the most out of all the $n$ cards and that card is my favourite. I consider the cards one by one, giving each an integer score, where the higher the score means the more I like that card. There are no ties in scores. The game is such that once I am done considering the $k^{th}$ card I lose the opportunity to select it as my favourite card forever. Suppose the candidates are considered in random order, chosen uniformly at random from all $n!$ possible orderings.
Current plan: consider the first $m$ cards, find the max score among them and then discard them. After the $m^{th}$ card, choose the first card who receives a higher score than the maximum from $m$ cards to be the favourite.
Let $E$ be the event that I choose my most preferred card as my favourite. Let $E_i$ be the event that the $i^{th}$ card is the most preferred and i choose it as my favourite. Find Pr[$E_i$] and show that Pr[$E_i$] = $\frac{m}{n} \sum_{j=m+1}^{n}\frac{1}{j-1}$
I have no idea how to begin solving this sum. Any intuition would be nice.