Ruby ternary condition seems to be ignored when not inside parens?

I'm trying to understand why converting this if-then-else line to the ternary expression (?:) didn't work. I know it may not be the most readable code, but I want to understand what's going on.

   if a = Artist.find_by(id: params[:artist_id]) then @songs = a.songs else redirect_to(artists_path, alert: "Artist not found") end

The artist_id in this test is set to garbage, so it exists, but no Artist exists with that id. The above if-then-else passes the tests, and all it good, but when I tried to make it a ternary expression like so:, it fails to work as I expected.

  a = Artist.find_by(id: params[:artist_id]) ? @songs = a.songs : redirect_to(artists_path, alert: "Artist not found")

which gives me the following failure:

1) songs when nested under artists /artists/:artist_id/songs displays the songs with valid artist
     Failure/Error: a = Artist.find_by(id: params[:artist_id]) ? @songs = a.songs : redirect_to(artists_path, alert: "Artist not found")

     NoMethodError:
       undefined method `songs' for nil:NilClass
     # ./app/controllers/songs_controller.rb:4:in `index'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/rack-1.6.4/lib/rack/etag.rb:24:in `call'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/rack-1.6.4/lib/rack/conditionalget.rb:25:in `call'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/rack-1.6.4/lib/rack/head.rb:13:in `call'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/rack-1.6.4/lib/rack/session/abstract/id.rb:225:in `context'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/rack-1.6.4/lib/rack/session/abstract/id.rb:220:in `call'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/railties-4.2.5/lib/rails/rack/logger.rb:38:in `call_app'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/railties-4.2.5/lib/rails/rack/logger.rb:20:in `block in call'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/railties-4.2.5/lib/rails/rack/logger.rb:20:in `call'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/rack-1.6.4/lib/rack/methodoverride.rb:22:in `call'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/rack-1.6.4/lib/rack/runtime.rb:18:in `call'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/rack-1.6.4/lib/rack/lock.rb:17:in `call'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/rack-1.6.4/lib/rack/sendfile.rb:113:in `call'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/railties-4.2.5/lib/rails/engine.rb:518:in `call'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/railties-4.2.5/lib/rails/application.rb:165:in `call'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/rack-1.6.4/lib/rack/urlmap.rb:66:in `block in call'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/rack-1.6.4/lib/rack/urlmap.rb:50:in `each'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/rack-1.6.4/lib/rack/urlmap.rb:50:in `call'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/rack-test-0.6.3/lib/rack/mock_session.rb:30:in `request'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/rack-test-0.6.3/lib/rack/test.rb:244:in `process_request'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/rack-test-0.6.3/lib/rack/test.rb:58:in `get'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/capybara-2.5.0/lib/capybara/rack_test/browser.rb:60:in `process'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/capybara-2.5.0/lib/capybara/rack_test/browser.rb:35:in `process_and_follow_redirects'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/capybara-2.5.0/lib/capybara/rack_test/browser.rb:21:in `visit'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/capybara-2.5.0/lib/capybara/rack_test/driver.rb:42:in `visit'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/capybara-2.5.0/lib/capybara/session.rb:232:in `visit'
     # /home/dapawn/.rvm/gems/ruby-2.3.3/gems/capybara-2.5.0/lib/capybara/dsl.rb:51:in `block (2 levels) in <module:DSL>'
     # ./spec/features/songs_spec.rb:13:in `block (4 levels) in <top (required)>'

If a is nil how can it be doing the true part of the ternary expression?

If I put parens around the condition like this, it works fine:

   (a = Artist.find_by(id: params[:artist_id])) ? @songs = a.songs : redirect_to(artists_path, alert: "Artist not found")

I figure it must some kind of precedence thing, but I just can't see it. Thanks n advance for taking the time to respond and help me learn.