This is easy in Kibana 5 search bar. Just add a filter
!(_exists_:"your_variable")
you can toggle the filter or write the inverse query as
_exists_:"your_variable"
In Kibana 4 and Kibana 3 you can use this query which is now deprecated
_missing_:"your_variable"
NOTE: In Elasticsearch 7.x, Kibana now has a pull down to select KQL or Lucene style queries in the search bar. Be mindful that syntax such as _exists_:FIELD
is a Lucene syntax and you need to set the pulldown accordingly.