Both queries will run in your current DB.

Take a look at this script

https://blogs.lessthandot.com/index.php/DataMgmt/DataDesign/how-to-get-information-about-all-databas#14

and modify to only include procedure you need.

>Hi,
>
>I am trying to find a stored procedure, by name, among many databases I have in my SQL Server. I tried two methods:
>

>SELECT * 
>FROM 
>    INFORMATION_SCHEMA.ROUTINES 
>WHERE 
>    ROUTINE_NAME LIKE '%MySP_Name%'
>

>
>

>select * 
>from 
>   sys.procedures 
>where 
>   name like '%MySP_Name%'
>

>
>Neither one returns a query. Does it mean I don't have this SP in any DB? Or should I try a different approach?
>
>TIA