I have an algorithm which, basically given an array of $n$ numbers, checks if there is any repeated numbers in the array, and returns true if there is and false otherwise.
It uses a direct access table (hashing function $h(x)=x$), which makes the running time linear. So it creates a new array, initializes all values to false, then iterates through the given array, and since each value is an index to the hash table, it accesses that array location and changes it to $1$. If it is already a $1$, then you know that it is a repeated number.
But when getting the expected running time, you need to first define a probability space. This is the part I am confused about. How can you define a probability of a number being repeated in A, if you are just given an array with arbitrary numbers?