As you noted it depends on the individual and what happened.
It's not uncommon for many couples to have been "emotionally divorced" long before becoming "legally divorced".
They may have already been sleeping in separate rooms, barely talking to one another, and essentially living as roommates.
One of them decides that life is passing her or him by and sees no need for them to continue as a married couple.
In this instance one or both of them might embrace their newfound freedom, dating, and exploring new relationships.
Their only regret is they waited so long in making their decision!
On the other hand if you believed you had a "happy marriage" and one day your spouse walks in to tell you they want a divorce that's a shock to the system!
Another possibility is you catch your spouse cheating and that is a "deal breaker" for you. In both of those instances one may not be in any hurry to date or get involved with someone soon after.
Generally speaking if there is someone who wanted to stay married they're less likely to rush out and jump into the dating the world.
When my first marriage ended in divorce we both started dating others almost immediately. The marriage had been in a deep coma for a while. We had separate bedrooms and phone lines in the house.
We were married in name only prior to making it a legal dissolution.
When it's all said and done a divorce is a public admission that someone (made a mistake in the mate selection area) of their life.
Human beings make mistakes including dating and choosing the wrong mate for themselves. Hopefully one learns from their mistake.
Every ending is a new beginning!