The second derivative of the call price at K gives the probability of that strike (implied probability density).
In practice, what adjustments or acknowledgements (if any) need to be made to produce a IPD with puts?
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By call-put parity, the second derivative of a European call option price with respect to strike is strictly equivalent to that of a European put.
So, yes: the result, known as the Breeden-Litzenberger identity, stays unchanged.