Apply a Fudge Factor
The proper way to deal with reduced team capacity is to apply a fudge factor to the team's planned story points for the Sprint. The size of the time box doesn't change, but the planned capacity for the time box should. Since the Development Team is responsible for accepting only the stories it expects to be able to complete into each Sprint, the team should use velocity as an input to estimating capacity rather than using it as a fixed management target.
The team is in the best position to estimate the reduction in its capacity; there's no fixed formula that will work in all situations. However, as is common in project management, the limiting factor is often your largest resource constraint: if the Product Owner will be unavailable for 60% of the Sprint, it is unlikely that the team can do more than 40% of its typical velocity, and perhaps even less if the holiday absences don't overlap.
For example, suppose your team averages 20 story points per Sprint. For the holiday Sprint, the team estimates that its capacity will be reduced by 75%. The team should therefore only accept 5 story points into the Sprint during Sprint Planning.
Recalculate Each Sprint
If you have more than one Sprint over your holiday period, then you should re-estimate and re-apply the fudge factor to your rolling velocity calculations each Sprint. The impact in your long-term velocity metrics is generally negligible, but the accuracy of your short-term estimates often improve by acknowledging the V-shaped changes in the team's capacity over the relevant time period.
Don't Discard the Metric
If you properly include the reduced-capacity Sprint in your trailing-average or annualized velocity metrics, you will end up with a much more accurate view of your project's real capacity over time. It may be tempting to exclude the holiday Sprint from your velocity calculations as a one-off, but discarding historical data is likely to skew your long-term estimates, and there will of course be other holidays or capacity issues in the future.
The point of velocity is that it reflects a sustainable average over time. Team capacity fluctuates, but if you keep the focus on the sustainable center of your bell curve then the majority of your Sprints will be a success.