[markov_chain_I] Move example subsections to sphinx-proof examples

[Jiarui-ZH]

@jstac, currently the markov_chain_I lecture has a lot of examples subheadings and can be a bit confusing to read. It was suggested by @mmcky that we could try use the proof domain and utilise {prf:ref} (https://sphinx-proof.readthedocs.io/en/latest/syntax.html) to make them look neater.

[jstac]

Good idea!

[mmcky]

@Jiarui-ZH - the one limitation sphinx-proof has at the moment is that they cannot contain executable code cells (you can show code but not execute it as jupyter restricts executable code to be at the root level of a document).

On a first pass you will want to migrate to https://sphinx-proof.readthedocs.io/en/latest/syntax.html#examples that don't have executable code.

I have been doing some work on sphinx-proof this week to update styles, and I will try to add support for gated directives next week -- which is required for supporting executable code blocks.

[mmcky]

executablebooks/sphinx-proof#108