When applying the noisy channel algorithm to real-word spelling correction, a simple approach to estimate the channel probability is to assume that the probability of the user writing the intended word correctly is $$ \alpha $$. The remaining probability mass, $$ 1 - \alpha $$, is then distributed evenly over all other candidate corrections $$ C(x) $$:

Channel Probability Estimation for Real-Word Correction

The algorithm takes the input sentence $$X=\{x_{1}, x_{2},..., x_{k},..., x_{n}\}$$ and generates a set of candidate words $$C(x_{i})$$ for each word $$x_{i}$$. The candidates include every word with a small edit distance from $$x_{i}$$. Then we pick the sentence with the highest language model probability. Each sentence is scored by the noisy channel model as follows:

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Detecting and correcting spelling errors even if they accidentally result in an actual
real word. 

This can happen from typographical errors (insertion, deletion, transposition) that accidentally produce a real word, or cognitive errors where the writer substituted the wrong spelling of a homophone or near-homophone. It is a much more difficult task than non-word errors correction since any word in the input text could be an error.

Real word spelling correction

An on-going but a helpful book resource about NLP
https://web.stanford.edu/~jurafsky/slp3/

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