Independence of holding time and next state in continuous-time Markov chain 
*

*In a continuous-time Markov chain, I was wondering why the holding time and the next state are independent? Are the independence a conditional one given the current state?

*Quoted from Ross's Stochastic processes:

The amount of time the process spends in state $i$, and the next state visited, must be independent random variables. For if the next state visited were dependent on $\tau_i$, then information as to how long the process has already been in state $i$ would be relevant to the prediction of the next state—and this would contradict the Markovian assumption.

One can also find identical claim at another book here with more
context available.
I don't understand why if the two are dependent, the Markov property
is violated.
Thanks and regards!

The next state depends on the recent states, not how long you stayed in them. Notice that this is implicit in the state transition matrix.
