What is meant by the monotonicity of probability? Give a practical example.

Example 1: what is the meaningof noremap

remap is an option that makes mappings work recursively. By default it is on and I'd recommend you leave it that way. The rest are mapping commands, described below:

:map and :noremap are recursive and non-recursive versions of the various mapping commands. What that means is that if you do:

:map j gg
:map Q j
:noremap W j
j will be mapped to gg. Q will also be mapped to gg, because j will be expanded for the recursive mapping. W will be mapped to j (and not to gg) because j will not be expanded for the non-recursive mapping.

Now remember that Vim is a modal editor. It has a normal mode, visual mode and other modes.

For each of these sets of mappings, there is a mapping that works in normal, visual, select and operator modes (:map and :noremap), one that works in normal mode (:nmap and :nnoremap), one in visual mode (:vmap and :vnoremap) and so on.

For more guidance on this, see:

:help :map
:help :noremap
:help recursive_mapping
:help :map-modes

Example 2: what is the meaningof noremap

For each of these sets of mappings, there is a mapping that works in normal, visual, select and operator modes (:map and :noremap), one that works in normal mode (:nmap and :nnoremap), one in visual mode (:vmap and :vnoremap) and so on.

For more guidance on this, see:

:help :map
:help :noremap
:help recursive_mapping
:help :map-modes