I can’t figure out what the notation $ [x \neq k ]$ means. Here’s a bit of context:

The formula is: $ Pr[A_i^k = 1] = \frac{[i\neq k]}{|k-i| + 1} = \begin{cases} \frac{1}{k-i+1} \text{ if } i \lt k \ 0 \text { if } i = k \ \frac{1}{i-k+1} \text{ if } i \gt k \end{cases}$

and is part of a chapter where the average expected time of operations of a randomised treap are proved.

$ A_i^k$ is an indicator variable defined as $ [ x_i \text{ is a proper ancestor of }x_k ]$ where $ x_n$ is the node with the $ n$ -th smallest search key. That probability comes up because $ \text{depth}(x_k) = \sum_{i=1}^{n} A_i^k$ and $ \mathbf{E}[\text{depth}(x_k)] = \sum_{i=1}^nPr[A_i^k = 1]$ .

I have no access to the pages that explain the notation since I’m studying from a pdf of a few pages taken from a book.