Query syntax on conditional column joins

I have two tables ProductRatio and Products, here is some sample data
ProductRatio
Category     Group       ProductID  Ratio
NULL         NULL        NULL       0.12
Alpha                               0.15
Alpha        Group1                 0.22
Alpha        Group1      123        0.27

Products
Category     Group       ProductID  Ratio
Alpha        Group1     123        
Alpha        Group2
Generic      Group1

I need to update the Products table Ratio column such that
If there is an exact match between Category, Group, and ProductID from the ProductRatio table then use that value.
If one does not exist use the Category and Group value.
If that does not exist just use the Category value,
If that is not there than default to the NULL value ,which in this case is 0.12

Based on this hierachy the values updated for ratio column in the Products table would be
Products
Category     Group       ProductID  Ratio
Alpha        Group1     123         0.27
Alpha        Group2                 0.15
Generic      Group1                 0.12