Giving a regular expression for a situation of a question
Here's a rough sketch: let $S_a, S_b, S_c$ be the set of valid strings of the language starting with $a, b, c$ respectively. Observe that:

$\qquad S_b = ((a^* + c^*)b)^*$

Furthermore:

$\qquad S_a = aS_a + bS_b$

and symmetrically for $S_c$. Therefore we may replace $S_b$ in the latter, obtaining a "recursive" equation solvable by Arden's lemma.