Will the vacation home be included in his probate estate

Kate and her brother Chris decided recently to purchase a vacation home together. They both want to use the vacation home to take their families for an annual vacation and then rent the vacation home using VRBO or Airbnb. The price for the vacation home was $450,000. Since Chris expects to use the vacation home 80% of the time and Kate 20% of the time, Chris contributed $360,000 and Kate contributed $90,000. Their ownership percentage equals their contribution percentage.
How do Kate and Chris own the vacation home?
Assuming that Chris dies unexpectedly, will the vacation home be included in his probate estate? Why?
If so, what is the vacation home’s value in Chris’ probate estate?
Will the vacation home be included in Chris’s gross estate?Why?
If so, what is the vacation home’s value in Chris’ gross estate?

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